These Simple Equations Are Levels of an Infinite Pattern Combo Class 2023-02-13 | You probably know 2+2 = 2x2, and you might know 1+2+3 = 1x2x3, but did you know those equations are connected and are two levels within an infinite family of similar equations? Let me show you some crazy facts, graphs, and mysteries that are hiding within this cool number pattern!I only listed “solutions” for up to "level" 11, so leave a comment if you figure out the solutions for future levels, or if you figure out any simple proof for how one of the layer’s solutions are the only possible solutions of that layer. It’s a fun challenge for the brain! The main “question/puzzle” of this episode doesn’t have an official name (it’s an underrated concept) but can be described as “which multisets of positive integers have an equal sum and product?” (or replace "positive integers" with "numbers" in that if you want to include the infinite spectrum of non-integer solutions).I made the graphs that are in this episode on the website Desmos (a useful free graphing calculator). Note that the non-integer coordinate numbers they are showing are approximations, and many of them would have infinite decimals. Also, part of the soundtrack in this episode is a beat I made on a livestream from scratch, to show how I make my soundtrack beats. You can see that on my bonus @Domotro channel here: www.youtube.com/watch?v=DPGLPY-3lXgCheck out my Patreon at patreon.com/comboclass if you want to support the channel, get some cool bonus content (like behind-the-scenes clips, my music, etc) and get your name on a whiteboard in the Grade -1 finale! Thanks a lot to all of my supporters there: Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Beugul.If you use Discord, join us on the Combo Class channel where there are lots of fun conversations going on: discord.gg/cHHvDcPPucThere's also a subreddit at reddit.com/r/comboClassAnd make sure you're also subscribed to my other channel @Domotro for my shorts, livestreams, and bonus videos.By the way, if you happen to have any broken clocks (or spare dice) and want them in the background of the Combo Classroom, you're in luck. I'll be starting a PO Box later this month for people to send me stuff like that.[DISCLAIMER: DO NOT TRY TO COPY ANY OF THE PARTS OF THIS EPISODE INVOLVING FIRE. In general, never copy any physical actions you see in Combo Class, such as anything involving fire, tools, or other science experiments.]
The Easy Shortcut to Translate Numbers Into Other Bases Combo Class 2024-12-24 | The first part of this video is a refresher about how to translate FROM other bases. Then most of the video is about a technique for translating INTO other bases (which I haven't covered before). Timestamps of different parts:0:00 - the two directions we could translate1:34 - the patterns of "basic bases" and the easier direction to translate5:33 - the technique to solve the harder direction to translateCatch up on the earlier episodes of Grade -3 with this chronological playlist:youtube.com/playlist?list=PLsATqXCEHAboWuDWuwrPGA0ZsiGNPOOvd(the "playlists" section of this channel also has playlists for Grade -1 and Grade -2).Thanks to my Patreon supporters (and supporters on the Youtube memberships on my @Domotro channel). See the credits at the end of this episode for all the names! Consider supporting Combo Class here: patreon.com/comboclassCatch up on the previous grade with this chronological playlist of Grade -2:youtube.com/playlist?list=PLsATqXCEHAbpDaoO9SCY3T9l4ak98kM2F(there is a playlist for Grade -1 on the channel also)Bonus channel:youtube.com/@DomotroDiscord: discord.gg/nMxjCEhhFnSubreddit: reddit.com/r/comboClassCombo Class was created by me (Domotro). This episode was directed, edited, and soundtracked by me. The background nature shots (during the voiceover parts) were filmed by me, and the classroom/garden parts with me on camera were filmed by Carlo Trappenberg.Some of the topics in this video include: the easier direction of translating into base ten from another base, the trickier direction of translating into other bases from base ten (and a cool shortcut involving division and remainders to help with it) , base ten, base six, base twelve, standard positional numeral systems, how each base considers itself base 10, how numbers of the form 100 and 1000 and 10000 and etc. relate to perfect powers, and more.Disclaimer: Do not copy any potentially dangerous actions you may see in these videos, such as any actions related to fire, glass, or tools.
The Fundamental Families of the Most Divisible Numbers Combo Class 2024-12-14 | Let me tell you about an interesting web of number families related to the most divisible numbers ever....0:00 - two mysterious sequences2:45 - two super-divisible sequences5:00 - an assortment of related number names6:37 - explaining the first layer of sequences7:17 - explaining the second layer of sequences9:50 - explaining the third layer of sequences12:47 - ways that these numbers could be important15:40 - outro/creditsPrevious episode about fractals: youtu.be/VE-lKj9tF4kThanks to my Patreon supporters (and supporters on the Youtube memberships on my @Domotro channel). See the credits at the end of this episode for all the names! Consider supporting Combo Class here: patreon.com/comboclassPlaylist of all Grade -2 episodes in chronological order:youtube.com/playlist?list=PLsATqXCEHAbpDaoO9SCY3T9l4ak98kM2FBonus channel:youtube.com/@DomotroDiscord: discord.gg/nMxjCEhhFnSubreddit: reddit.com/r/comboClassCombo Class was created by me (Domotro). This episode was directed, edited, and soundtracked by me. The background nature shots (during the voiceover parts) were filmed by me, and the classroom/garden parts with me on camera were filmed by Carlo Trappenberg.Some of the types of numbers covered in this episode include: prime numbers, composite numbers, highly composite numbers, superior highly composite numbers, abundant numbers, highly abundant numbers, superabundant numbers, and colossally abundant numbers.Disclaimer: Do not copy any potentially dangerous actions you may see in these videos, such as any actions related to fire, glass, or tools.
The Hidden Fractals in Pascals Triangle Combo Class 2024-11-30 | (0:00) Part 1: The Sierpinski Triangle(4:36) Part 2: Pascal's Triangle(8:22) Part 3: How These Triangles Are ConnectedI created all the graphics in this video myself.Check out the previous episode (the intro to Grade -3) here:youtu.be/4gdP5_cTuGUPlaylist of all Grade -2 episodes in chronological order:youtube.com/playlist?list=PLsATqXCEHAbpDaoO9SCY3T9l4ak98kM2FBonus channel:youtube.com/@DomotroThanks to my Patreon supporters (and supporters on the Youtube memberships on my Domotro channel). See the credits at the ending of this episode for all of the names! Consider supporting Combo Class at the link below:patreon.com/comboclassDiscord: discord.gg/nMxjCEhhFnSubreddit: reddit.com/r/comboClassCombo Class was created by me (Domotro). This episode was directed, edited, and soundtracked by me, and was filmed by me and Carlo Trappenberg. I also made all of the images/graphics in the video.Topics in this episode include: a description of fractals and self-similarity, a cool fractal-esque vegetable (often called "romanesco broccoli" or "romanesco cauliflower"), how to approximate a "Sierpinski triangle" with an iterated process that approaches it, some strange traits about non-integer dimensions of fractals, how "Pascal's triangle" can be created from binomial coefficients or from a simple rule about adding numbers together, some ways in which Pascal's triangle relates to triangular/tetrahedral numbers and the Fibonacci sequence and the powers of 2, hexagonal grids, how to find the Sierpinski triangle in Pascal's triangle, a family of triangle-related fractals, modular arithmetic such as mod 2 and mod 3, and more.Disclaimer: Do not copy any potentially dangerous actions you may see in these videos, such as any actions related to fire, glass, or tools.
Welcome to Grade -3 of Combo Class! Combo Class 2024-11-19 | This is the first episode of Grade -3. The first couple minutes of this contains a brief overview of Combo Class and the new grade, and then most of the video is facts/proofs about the number 3 (skip to 1:58 if you just care about that part).Check out the previous episode (the Grade -2 finale) here:youtu.be/y57lg6U-Yd4Playlist of all Grade -2 episodes in chronological order:youtube.com/playlist?list=PLsATqXCEHAbpDaoO9SCY3T9l4ak98kM2FBonus channel:youtube.com/@DomotroThanks to my Patreon supporters (and supporters on the Youtube memberships on my Domotro channel). See the credits at the ending of this episode for all of the names! Consider supporting Combo Class at the link below:patreon.com/comboclassDiscord: discord.gg/nMxjCEhhFnSubreddit: reddit.com/r/comboClassCombo Class was created by me (Domotro). This episode was directed, edited, and soundtracked by me, and was filmed by Carlo Trappenberg, with additional filming by me and Kira S.M. Norwood.Disclaimer: Do not copy any potentially dangerous actions you may see in this video, such as any actions related to fire, glass, or tools.Timestamps:0:00 - introduction1:58 - facts and proofs about the number 37:32 - conclusion
The Grade -2 Finale Combo Class 2024-11-05 | This is the final episode of Grade -2 of Combo Class. It is like a documentary about the past era of my life (and about the past grade, although most parts are made entirely of unseen footage). I spent a long time making this video and I hope you watch the whole thing, but here are timestamps of its different chapters:0:00 - Part 1: Introduction1:58 - Part 2: Injuries6:09 - Part 3: Adventures8:22 - Part 4: Animals15:44 - Part 5: Plants20:46 - Part 6: Evolutions25:51 - Part 7: Camping28:27 - Part 8: Secrets30:18 - Part 9: Cycles33:58 - Part 10: ConclusionTo be continued soon in Grade -3....Thanks to my Patreon supporters (and supporters on the Youtube memberships on my Domotro channel). See the credits at the ending of this episode for all of the names! Consider supporting Combo Class at the link below:patreon.com/comboclassDiscord: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassBonus channel:youtube.com/@DomotroThe previous grade's finale:youtu.be/RLhNlK-MUHgPlaylist of all Grade -2 episodes in chronological order:youtube.com/playlist?list=PLsATqXCEHAbpDaoO9SCY3T9l4ak98kM2FThis episode was directed, edited, and soundtracked by me (Domotro), and filmed by me, Carlo Trappenberg, Kira MH Norwood, and Rishi Amutas.Disclaimer: Do not copy any potentially dangerous actions you may see in this video, such as any actions related to fire, glass, or tools.
The Mysterious Pattern I Found Within Prime Factorizations Combo Class 2024-09-12 | In this special episode (the longest one I've created yet) let me show you an interesting pattern I recently found, and all of the cool mathematical connections I've been able to deduce about it.... Timestamps of different chapters:0:00 - My Explorations Into Primeglitching3:29 - Explanation of the Main Pattern9:18 - Discoveries Among the First 50 Numbers14:36 - Discoveries Among Larger Numbers19:57 - Finding the Other Research About This27:38 - What I Could Deduce About the General Pattern32:30 - What I Could Deduce About Fixed Points42:13 - What I Could Deduce About Two-Number Cycles50:47 - Ideas for Larger Cycles and General Proofs55:12 - Extending to Fractions and Square Roots1:05:22 - Other Forms of Potential PrimeglitchingI only came across this pattern about a month ago, so I'm sure I'll realize or deduce other things about it when I return to the problem later. I'll probably investigate this (and other primeglitching patterns) more on my bonus @Domotro channel so make sure you're tuned in there as well.... And if any of you find or prove anything about this concept yourself, leave a comment and/or send me an email at combouniversity@gmail.com (or just write your own paper about it and credit me somewhere!)Corrections/clarifications:- One of the diagrams shows 48 going to 15 and then 24, but it doesn't actually pass by 15 (48 goes directly to 24).- In an early example, I showed 1050 going to 840 but it really goes to 672 (the general point about it shrinking overall it still true).Next episode will be the Grade -2 finale! (Before we enter Grade -3 soon). The finale will be like a documentary about making this grade, including lots of interesting behind-the-scenes moments that didn't make it into episodes, among other things...In the meantime, make sure you've checked out my previous Grade -1 finale/documentary: youtu.be/RLhNlK-MUHgAnd here's a playlist of all of Grade -2 so far (in order) if you want to make sure you've seen them all: youtube.com/playlist?list=PLsATqXCEHAbpDaoO9SCY3T9l4ak98kM2FSpecial thanks to my current supporters on Patreon! Max, George Carozzi, Chandler Smith, Eric Brodeur, Henry Spencer, Jon Mandarin, Mitch Harding, Tybie Fitzhugh, Joshua S, Julius 420, Peter Offutt, Quinn Moyer, Beugul, Stan Seibert, Dave Brondsema, Florian, Jan Bosenberg, Mathias Ermatinger, terry, William Hawkes, Christopher Masto, Claudio Fanelli, Craig Butz, Harry Cruse, Joost Boesburg, Kali OmegaRogue, Michael Friemann, The Green Way, Mack, cat, Stephen Davies, and Mackenzie Newman! I WILL BE THANKING ALL PATREON SUPPORTERS (NEW AND OLD) AND WRITING YOUR NAMES ON A WHITEBOARD NEXT EPISODE. If you want to get your name on that list and help support this channel (which helps me keep making videos without any brand advertisements) and get some bonus content, check out the Patreon here: patreon.com/comboclassIn case anybody searches any of these terms, some topics that show up in this episode include: prime numbers, prime factorizations, something I call "primeglitching", the OEIS (Online Encyclopedia of Integer Sequences), squarefree numbers, powerfree parts of numbers, factors/divisors, extended prime factorizations into rational numbers like fractions as well as some irrational numbers like square roots, natural density, tree-like visualizations of numbers, and much more.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg. The visuals of the number trees were designed by Stick.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
The Mathematics of 2024s Rare Insect Swarms Combo Class 2024-08-14 | This is a short episode about the mathematical reason why a rare natural event happened this year.In a week or two, I’ll have a longer number theory episode out, and then after that will be the Combo Class Grade -2 finale (and then the beginning of Grade -3).Check out my @Domotro channel for my bonus content, such as shorts and livestreams.Special thanks to my current supporters on Patreon! Max, George Carozzi, Chandler Smith, Eric Brodeur, Henry Spencer, Jon Mandarin, Mitch Harding, Tybie Fitzhugh, Joshua S, Julius 420, Peter Offutt, Quinn Moyer, Beugul, Stan Seibert, Dave Brondsema, Florian, Jan Bosenberg, Mathias Ermatinger, terry, William Hawkes, Christopher Masto, Claudio Fanelli, Craig Butz, Harry Cruse, Joost Boesburg, Kali OmegaRogue, Michael Friemann, The Green Way, Mack, cat, Stephen Davies, and Mackenzie Newman! If you want to get your name on that list and help support this channel (which helps me keep making videos without any brand advertisements) and get some bonus content, check out the Patreon here: patreon.com/comboclassThis episode is about a large migration of Brood XIII and Brood XIX of periodic cicadas which run on 13-year and 17-year cycles, which emerged at the same time throughout the Eastern portion of the United States during this year 2024. This last happened in 1803, and will next happen in 2245, exactly 221 years in each direction. The reason for this relates to prime numbers and semiprime numbers.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
How to Prove a Number is Irrational Combo Class 2024-08-02 | In this episode, I'll show you some surprisingly simple proofs that certain numbers (like the square root of 2) are “irrational”, and explain what has been proven about other numbers like pi, e, and “Legendre’s constant”. Timestamps of different chapters: 0:00 - Introduction1:50 - Proving a Logarithm is Irrational3:50 - Proving a Square Root is Irrational9:26 - What About Pi and E?11:36 - The Funny Tale of Legendre’s Constant15:13 - ConclusionSome previous episodes I mentioned in this one:- about continued fractions: youtu.be/YCJ99liapCQ- about why there are more irrationals than rationals: youtu.be/6NgI0qT9r6kSpecial thanks to my current supporters on Patreon! Max, George Carozzi, Chandler Smith, Eric Brodeur, Henry Spencer, Jon Mandarin, Mitch Harding, Tybie Fitzhugh, Joshua S, Julius 420, Peter Offutt, Quinn Moyer, Beugul, Stan Seibert, Dave Brondsema, Florian, Jan Bosenberg, Mathias Ermatinger, terry, William Hawkes, Christopher Masto, Claudio Fanelli, Craig Butz, Harry Cruse, Joost Boesburg, Kali OmegaRogue, Michael Friemann, The Green Way, Mack, cat, Stephen Davies, and Mackenzie Newman! If you want to get your name on that list and help support this channel (which helps me keep making videos without any brand advertisements) and get some bonus content, check out the Patreon here: patreon.com/comboclassCombo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassThis episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
The Insane World of Polygon Packings Combo Class 2024-07-07 | Let me show you some surprising things about how squares and other polygons fit into different spaces!0:00 - Homemade Demonstrations of the Square Packing Problem7:06 - Digital Images of The Craziest Square Packings14:24 - Packing Other Types of PolygonsHere are the websites that I used images from:erich-friedman.github.io/packingkingbird.myphotos.cc/packing/squares_in_squares.htmlkingbird.myphotos.cc/packing/squares_in_squares__compared.htmlIn the images I included, there are some notes attached (from the original websites). To clarify some terms: they use "s" to describe how many times longer the big square's side-length is compared to the small squares (or equilateral triangles), and use "r" to describe the radius of the larger circle in terms of smaller shapes. Most of the images also clarify whether they have been proven, or if they've just been found (which means they are the current best-known configuration but another weird arrangement could possibly beat them later).Special thanks to my current supporters on Patreon! Max, George Carozzi, Chandler Smith, Eric Brodeur, Henry Spencer, Jon Mandarin, Mitch Harding, Tybie Fitzhugh, Joshua S, Julius 420, Peter Offutt, Quinn Moyer, Beugul, Stan Seibert, Dave Brondsema, Florian, Jan Bosenberg, Mathias Ermatinger, terry, William Hawkes, Christopher Masto, Claudio Fanelli, Craig Butz, Harry Cruse, Joost Boesburg, Kali OmegaRogue, Michael Friemann, The Green Way, Mack, cat, Stephen Davies, and Mackenzie Newman! If you want to get your name on that list and help support this channel (which helps me keep making videos without any brand advertisements) and get some bonus content, check out the Patreon here: patreon.com/comboclassCombo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, this episode is about some crazy geometry that some may consider cursed (and/or beautiful), related to the most efficient ways to pack certain polygons into shapes, such as square packings, triangle packings, circle packings, cube packings, combinations of those, and more!This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
Crazy Coconut Chronicles Combo Class 2024-06-24 | In this snack break / field trip, we will learn many things about coconuts.... (I'll also have a new mathematical episode out in about a week).Special thanks to my current supporters on Patreon! Max, George Carozzi, Chandler Smith, Eric Brodeur, Henry Spencer, Jon Mandarin, Mitch Harding, Tybie Fitzhugh, Joshua S, Julius 420, Peter Offutt, Quinn Moyer, Beugul, Stan Seibert, Dave Brondsema, Florian, Jan Bosenberg, Mathias Ermatinger, terry, William Hawkes, Christopher Masto, Claudio Fanelli, Craig Butz, Harry Cruse, Joost Boesburg, Kali OmegaRogue, Michael Friemann, The Green Way, Mack, cat, Stephen Davies, and Mackenzie Newman! If you want to get your name on that list and help support this channel (which helps me keep making videos without any brand advertisements) and get some bonus content, check out the Patreon here: patreon.com/comboclassCombo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: botany, plants, fruits, seed propogation, the island Kauai on Hawaii, regular coconuts, young coconuts, old coconuts, and more!This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Rishi Amutas and Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
Equations That Are True in Many Bases Combo Class 2024-05-16 | Let me take you on a journey through some equations that are true in many different ways, to show some patterns I realized about the interconnected nature of different bases!Special thanks to my current supporters on Patreon! Max, George Carozzi, Chandler Smith, Eric Brodeur, Henry Spencer, Jon Mandarin, Mitch Harding, Tybie Fitzhugh, Joshua S, Julius 420, Peter Offutt, Quinn Moyer, Beugul, Stan Seibert, Dave Brondsema, Florian, Jan Bosenberg, Mathias Ermatinger, terry, William Hawkes, Christopher Masto, Claudio Fanelli, Craig Butz, Harry Cruse, Joost Boesburg, Kali OmegaRogue, Michael Friemann, and The Green Way! If you want to get your name on that list and help support this channel (which helps me keep making videos without any brand advertisements) and get some bonus content, check out the Patreon here: patreon.com/comboclassCombo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: different numeral bases, quantities vs digit representations, equations that are true in many bases, polynomial functions, alien mathematics, and much more.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg and Rishi Amutas.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
The Most Underrated Concept in Number Theory Combo Class 2024-05-05 | This is probably my favorite video I've made yet. It's about an underrated mathematical concept known as "integer complexity" and my personal journey to discover it.0:00 - Introduction1:20 - A Mathematical Question I Stumbled Into3:23 - Discoveries Among the First Dozen Numbers6:49 - What is the Largest Number We Can Build?11:19 - Number Webs With Mysterious Gaps13:54 - Incorporating Subtraction and Division17:23 - How I Found the Name of This Concept21:00 - Further Directions We Could Take This24:40 - A Philosophical Question I Stumbled Into27:27 - OutroductionClarifications and corrections:- When I draw the web of which numbers you can build with eight ones I forgot to draw a dot for 14, which should also be on that web.- During one of the whiteboard b-roll shots, I showed 4 as being built by "1+1+1+1+1" which is one too many ones.- Lots of comments on this video mention that exponentiation would make things have lower costs. That's true, but I wasn't including exponentiation here, because we have to define the exact mix of operations we are using at each point, not take any operations for granted (like, if we automatically allow exponentiation, why not automatically allow tetration?) so this video shows how I just began with addition/multiplication, then included subtraction, then included division. You could include exponentiation (which would change costs of course) if you wanted to look for other further patterns, and I'm sure there's interesting patterns to find there too (there are some OEIS entries related to that on Glenn Whitney's table I mentioned). However, you could also include any number of other operations if you chose (tetration, roots, logarithms, etc.).- For some reason, various comments on this video claimed that the integer complexity was always just equal to a number's prime factorization, which is not true.Special thanks to all of my supporters on Patreon! (Supporting the show not only helps me keep improving my content, but also lets me avoid needing to incorporate any product placements from brands in episodes) Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, Dave Brondsema, and Chandler Smith! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassCombo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: number sequences, the OEIS (or "Online Encyclopedia of Integer Sequences"), Mahler-Popken "integer complexity" and extensions to it, my fun personal mathematical journeys, and more.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Rishi Amutas and Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
Why There Are Multiple Sizes of Infinity Combo Class 2024-04-13 | In this episode I'll explain about how/why there are different sizes of "infinity", including concepts such as Cantor's Diagonal Argument, the Aleph Numbers, the Continuum Hypothesis, and more!0:00 - Intro1:37 - How Many Square Numbers Are There?2:51 - Surjective/Injective/Bijective Cats6:03 - How Many Integers Are There?7:28 - How Many Fractions Are There?12:46 - How Many Real Numbers Are There?13:36 - Cantor's Diagonal Argument19:54 - The Hierarchy of Aleph Numbers21:28 - The Continuum Hypothesis24:51 - OutroTo my Combo Lords: Sorry that some recent episodes have taken a while to finish. I’ve been in the process of semi-moving houses and other personal things (see the livestream videos on my bonus @Domotro channel for some details). My next episode may also take a couple weeks, since it’ll be a long one about what I consider to be the most underrated concept in number theory. After that, I can hopefully get back to a quicker release schedule. In any case, thanks for watching!Special thanks to all of my supporters on Patreon! (Supporting the show not only helps me keep improving my content, but also lets me avoid having any product placements from brands in episodes) Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, Dave Brondsema, and Chandler Smith! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassCombo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: countable vs. uncountable infinities, bijections and injective/sujective/bijective functions, the Aleph numbers like Aleph 0 and Aleph 1, Georg Cantor and Cantor's diagonal / diagonalization argument, the Continuum Hypothesis, and other topics related to "set theory" and different sizes/cardinalities of infinities.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
The Amazing Patterns of Modular Exponents Combo Class 2024-03-13 | In this episode, I'll show you some clock-like number tricks that reveal patterns about exponents, prime numbers, "pseudoprimes", other bases, and more! See below for timestamps of different parts (and related episodes I've made)0:00 - Introduction0:24 - An Interesting Trait About Last Digits2:47 - Connecting the Mathematics to Clocks6:09 - Why 0, 1, 5, and 6 Did a Special Thing9:30 - Interesting Symmetries Within Our Base11:15 - Prime Mods/Bases and Fermat's Little Theorem16:01 - Pseudoprimes and Carmichael Numbers19:27 - A Further Generalization / A Chaotic OutroHere are some previous episodes I've made related to modular arithmetic: (which can be watched either before or after this video)About modular multiplication: youtu.be/hH89nUGd6DU?si=d0vqjcJfexWO3bCkAbout modular division: youtu.be/Qh_SjdWnKpc?si=cJDZaMfSjYj0zcoxAbout "Wilson's theorem": youtu.be/jx2qGlNwiP4?si=zi4TAhrDDxJfj1za(And many of my other episodes are also related to modular arithmetic in more subtle ways!)Make sure you're also subscribed to my @Domotro channel for bonus content!Special thanks to all of my supporters on Patreon! (Supporting the show not only helps me keep improving my content, but also lets me avoid having any product placements from brands in episodes) Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you want to, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: exponents, modular arithmetic, modular multiplication, modular exponentiation, base ten and other numeral bases like base two (binary) and various others, mathematics related to clocks, prime numbers, pseudoprime numbers such as Fermat pseudoprimes, Carmichael numbers, Fermat's Little Theorem, Euler's (Totient) Theorem, and more!This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
The Most Powerful “Magic Cards” of All Time Combo Class 2024-02-16 | After lots of research about the oldest "trading card game", this video is my findings about the most powerful "Magic: the Gathering" cards of all time, and what they can teach us about game design:0:00 - Intro2:20 - Explaining the game rules7:57 - The color wheel of Magic9:38 - The "Power Nine" and the early years14:20 - The most imbalanced "cycle"16:25 - The different "formats" of Magic18:40 - What new players expect to be powerful21:48 - Analyzing the 35 "superbanned" cards33:40 - Investigating the 44 "hyperbanned" cards39:20 - The most powerful "ante" card43:23 - The important history of "companion" cards50:15 - The cards that broke other formats55:35 - My overall conclusions1:00:27 - OutroMake sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, here are playlists of each whole "grade" in chronological order: youtube.com/@ComboClass/playlistsHere's a few clarifications about things I said to be extra technical (although these mini clarifications don't invalidate this episode's main ideas)- I did have to oversimplify many things about this game's rules and history. It is very complicated and the episode would have been many hours if I included every technical detail. I tried my best to oversimplify it without saying any incorrect details.- While filming this episode, I tried to only damage non-valuable cards. And no, I don't own physical copies of any of the super-overpowered (or expensive) cards I showed images of on screen.- I said that Conspiracy cards start in the battlefield, but they are technically in a separate zone (although the overall concept is similar, that you begin the game with their effect for free)- I implied that Contract From Below lets you pick which card to ante, but it must be the first one of the eight (although that doesn't change the fact of how overpowered it is)- I said that "companion" cards would be the only cards in their separate zone, but typically you would have had other cards with them in the "sideboard" (although they were typically the only cards you could play from there in the midst of an ongoing game). Also, as an extra fact, when the designers changed the "companion" mechanic, it not only made you pay 3 mana, but also made the card stop by your hand first, where opponents could possibly remove it with instant-speed discard effects.Special thanks to all of my supporters on Patreon! (Supporting the show not only helps me keep improving my content, but also lets me avoid having any product placements from brands in episodes) Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you want to, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: Magic the Gathering, Magic Cards, Richard Garfield, Mark Rosewater, the Power Nine such as Black Lotus and Ancestral Recall and the moxes/moxen, Lurrus and the companion mechanic, Contract From Below and the ante mechanic, Pack Rat and the draft format, other formats such as Vintage and Legacy and Standard and Modern and Commander/EDH, and overall the most powerful Magic cards of all time and what they can teach us about game design.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg (who also helped with some of the editing).Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
Why 666 Isnt Cursed, But 6[6]6 Might Be Combo Class 2024-01-23 | Let me show you some cool mathematical properties of the number 666, some spooky things about its cousin 6[6]6, and analyze what it means to understand massive numbers as a human.Here's the previous episode I made about tetration if you want to learn more about hyperoperations: youtu.be/eVRJLD0HJcE?si=Q5lQ7614PpuGGS9uNote: When I've joked about the number 666 before in livestreams on my bonus channel, I've gotten comments saying that I apparently am going to hell or that I apparently hate Jesus. So, perhaps I will get some comments like that on this video too. It's true that I'm not very religious, moreso agnostic (or perhaps the first "comboist" haha) but to be clear, I do think many teachings attributed to the potential Jesus (such as loving your enemies and feeding the poor) are great ideals I fully agree with. So if you plan on commenting anything about how I apparently hate Jesus or whatever, please watch the whole video first (and think about whether you think I am a good human in general) before leaving whatever comments you want hahaha.Also, a little correction: when I wrote/said that 666 was the sum of the first 7 prime numbers each "cubed", that should have been "squared".Make sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, I've now made playlists of each whole "Grade" in chronological order: youtube.com/@ComboClass/playlistsSpecial thanks to all of my supporters on Patreon. Supporting the show not only helps me keep improving my content, but also lets me avoid putting any product placements in episodes. Brands have offered me money for me to advertise them during an episode on this channel but I want to avoid that unless/until necessary, so thank you to all of these supporters who keep our Grade -2 episodes from having any product placements in them! Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: the number 666 and another number 6[6]6, superstitions and superstitious beliefs about numbers, hypothetically unlucky or cursed or spooky numbers, hyperoperations such as addition and multiplication and exponentiation and tetration and pentation and hexation and beyond, googol and googolplex and larger numbers within the field of googology, something that I call sandwich numbers, other number theory terms and topics, and much more.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.
Extreme Egg Experiments Combo Class 2024-01-14 | In this "snack break", I test what happens when you cook eggs for longer than I could find any other research about!Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire. Make sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, I've now made playlists of each whole "Grade" in chronological order: youtube.com/@ComboClass/playlistsSpecial thanks to all of my supporters on Patreon. Supporting the show not only helps me keep improving my content, but also lets me avoid putting any product placements in episodes. Brands have offered me money for me to advertise them during an episode on this channel but I want to avoid that unless/until necessary, so thank you to all of these supporters who keep our Grade -2 episodes from having any product placements in them! Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: cooking, eggs, 7-hour eggs / seven hour eggs, a new 24-hour egg experiment (eggsperiment), other fun facts about eggs and various culinary things, how to make the different stages of soft-boiled and hard-boiled eggs, the maillard reaction with toast and meat and eggs, slow-cooker / crockpot egg cooking, ovens, fire, cats, and other fun things.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg, Penny Werner, Mark Zucker, and myself.
I Found a Simple Pattern That Encodes Different Bases Combo Class 2023-12-25 | While I was trying to invent a card game recently, I stumbled into some questions/answers that I realized were describing patterns about other numeral bases! Let me show you about something I call "numberations":0:00 - Part 0: Introduction1:48 - Part 1: What Are Numberations?4:43 - Part 2: Visualizations of Doubling8:11 - Part 3: Visualizations of Tripling10:37 - Part 10: Converting to Other Bases13:15 - Part 11: Finding the Missing Numbers15:48 - Part -1: Base Ten and Stranger Bases20:31 - Part -2: Outroduction(I'll add more applicable links to episodes I've made about bases here soon. If you're curious in the meantime, you can scroll through my Grade -1 and Grade -2 playlists for episodes with "base" in the name. And if you're curious about the livestream where I accidentally lit myself on fire, see the "live" tab on my @Domotro channel.)Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire. Note: although I did discover/realize all of the things in this episode myself, I'm sure other people have noted similar things throughout the history of mathematics. Since my description/visualization is slightly different than other ones I've encountered, I nicknamed the seeds of these patterns "numberations". I think it's a useful term; do you think we could ever get it into a dictionary?Make sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, I've now made playlists of each whole "Grade" in chronological order: youtube.com/@ComboClass/playlistsSpecial thanks to all of my supporters on Patreon. Supporting the show not only helps me keep improving my content, but also lets me avoid putting any product placements in episodes. Brands (not the company that makes Connect 4 haha) have offered me money for me to advertise them during an episode on this channel but I want to avoid that unless/until necessary, so thank you to all of these supporters who keep our Grade -2 episodes from having any product placements in them! Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: number theory, whole numbers, integers, base 2 / base two / binary, base 3 / base three / ternary, balanced ternary / balanced base 3, base ten / decimal, other different numeral bases and number systems / representations of numbers, a pattern I nicknamed "numberations", more!This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.
Artificial Intelligence vs. Mathematics Combo Class 2023-12-09 | In this episode, we'll look at some times when “artificial intelligence” has been hilariously stupid, and then some times when it has actually helped mathematicians!0:00 - Introduction1:16 - My Feelings About Technology2:32 - A Hilariously Stupid Robot8:17 - Hypotheses About Chatbots11:54 - The Map Coloring Problem18:23 - A Helpful (But Controversial) Robot24:10 - OutroductionNote: This episode took longer than usual to come out because I’ve been sick. I caught some germ around the time I filmed this, and it messed up my routine for a few weeks, although I'm mostly better now. The next episode may also take a little longer than usual, but then I hope to get closer to 1 episode per week!In this video's section about ChatGPT, I was using the latest free version (GPT-3.5) and not the paid version (GPT-4). Some people say the paid version would have been better, but the free version I used is what the media was mostly discussing and what the majority of users were using.Also, to note in advance: last time I acted silly with a computer/laptop in a video, some commenters thought I broke a functional computer and was being wasteful with technology. If you see any technology items break in my videos, assume they were already broken, unless I specify otherwise. I keep my actual functional computer a safe distance from my classroom when I'm filming episodes haha.Make sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, I've now made playlists of each whole "Grade" in chronological order: youtube.com/@ComboClass/playlistsSpecial thanks to all of my supporters on Patreon. Supporting the show not only helps me keep improving my content, but also lets me avoid putting any product placements in episodes. Brands (not the company that makes Connect 4 haha) have offered me money for me to advertise them during an episode on this channel but I want to avoid that unless/until necessary, so thank you to all of these supporters who keep our Grade -2 episodes from having any product placements in them! Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: calculators, robots, artificial intelligence, AI, ChatGPT, OpenAI, Wolfram Alpha, the four-color theorem / 4-color map theorem, the five-color theorem / 5-color map theorem, smart robots vs. dumb robots, computer helping and hurting mathematicians, cats, squirrels, flames, globes / spheres, donuts / toruses / coffee cups, and much more!This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is an episode of a show that is purely meant to provide entertainment and education. Also, do not copy the squirrel-feeding (my squirrels have a rare circumstance) without doing your own research first.
Whats the Opposite of the Number 2? Combo Class 2023-11-09 | Do numbers have antonyms? In this episode, we’ll take a mathematical (and philosophical) journey through different sorts of opposites and inverses.0:00 - A Philosophical Look at Opposites3:46 - Identity Elements vs. Absorbing Elements6:30 - Additive Inverses vs. Multiplicative Inverses8:53 - Exponential Inverses vs. Exponential Inverses10:19 - Left Identities vs. Right Identities12:19 - Why Addition and Multiplication Are So Important14:35 - Concluding Philosophies, Flames, and GratitudePLEASE DO NOT COPY ANY FIRE-RELATED ACTIVITIES YOU MAY SEE IN THIS EPISODE :)Make sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, I've now made playlists of each whole "Grade" in chronological order: youtube.com/@ComboClass/playlistsSpecial thanks to all of my supporters on Patreon. Supporting the show not only helps me keep improving my content, but also lets me avoid putting any product placements in episodes. Brands (not the company that makes Connect 4 haha) have offered me money for me to advertise them during an episode on this channel but I want to avoid that unless/until necessary, so thank you to all of these supporters who keep our Grade -2 episodes from having any product placements in them! Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics in this video include: the number 2 / two, the "real numbers", antonyms, opposites, reciprocals, additive vs. multiplicative inverses, multiple types of exponential inverses, negatives, fractions, identity elements, absorbing elements, fire, clocks, whiteboards, squirrels, and other assorted mathematics and philosophy and nature.This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg (apart from the scene near the end with the upside-down pumpkin which was filmed by Max Chervin).Disclaimer: Do NOT copy any dangerous-seeming actions involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is an episode of a show that is purely meant to provide entertainment and education. Also, do not copy the squirrel-feeding (my squirrels have a rare circumstance) without doing your own research first.
Is it Possible to Always Win at Connect 4? Combo Class 2023-10-26 | Is there a strategy that could win the game Connect 4 every time? Let me show you how this question leads to a bunch of surprising patterns, unsolved mysteries, and connections to other games like Tic-Tac-Toe and Chess! (See below for timestamps of different subtopics)0:00 - Introduction1:06 - Basic Rules and Human Strategies of Connect 44:39 - Zermelo's Theorem about Solvable Games5:58 - Tic-Tac-Toe, Tic-Tac-Two, and Adding "Gravity"9:22 - The Solvability of Chess10:57 - Strategy-Stealing Techniques13:46 - Why "Connect 3" Wouldn't Be Fun15:55 - Connect 4 on Different Board Sizes18:42 - The Mysterious Landscape of Known Solutions21:57 - How The First Move Can Determine Everything23:54 - Philosophies about Humans and Computers26:54 - OutroductionThanks for watching! I might analyze more games in future episodes from time to time, so let me know if there are any games you personally enjoy and/or would like to see me cover (I don't play video games much so I'm more likely to check out the math within board games or card games). A few games/puzzles I’ve written brainstorm notes about which might be parts of future episodes include: Tic-Tac-Toe, Checkers, Chess, Magic The Gathering, Poker, Sudoku, Othello / Reversi, Two Not Touch (a.k.a. Star Battle), Rock-Paper-Scissors (yes it actually has "strategy" haha), and some board games I invented myself.Here's a website page from the computer scientist John Tromp that I quoted some data from in this episode: tromp.github.io/c4/c4.htmlSlight correction about Zermelo's theorem: there's one extra restriction about which games it describes, which is that they must be "finite" games, as opposed to games that could continue for infinitely long.Make sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, I've now made playlists of each whole "Grade" in chronological order: youtube.com/@ComboClass/playlistsSpecial thanks to all of my supporters on Patreon. Supporting the show not only helps me keep improving my content, but also lets me avoid putting any product placements in episodes. Brands (not the company that makes Connect 4 haha) have offered me money for me to advertise them during an episode on this channel but I want to avoid that unless/until necessary, so thank you to all of these supporters who keep our Grade -2 episodes from having any product placements in them! Evan Clark, Max, George Carozzi, Peter Offutt, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Combo Class Discord server: discord.gg/cHHvDcPPucSubreddit: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms to learn about them, some topics mentioned in this video include: the mathematics of game theory, Zermelo’s theorem about two-person games without randomization and with perfect information, Connect 4 / Connect Four strategy and solvability, Connect 4 on various different sizes of board, solvability of chess, tic-tac-toe and strategy-stealing arguments, philosophy of computers vs. humans remembering data, fire, squirrels, and more!This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.Disclaimer: Do NOT copy any dangerous-seeming actions involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is an episode of a show that is purely meant to provide entertainment and education. Also, do not copy the squirrel-feeding (my squirrels have a rare circumstance) without doing your own research first.
Multiplication Tables Are Taught Wrong Combo Class 2023-10-13 | Let me explain how multiplication tables are often taught wrong, and show a bunch of underrated patterns within them:0:00 - Part 1: Metamemorization2:26 - Parts 2 and 3: Primes and Composites5:58 - Parts 4, 8, and 9: Squares and Almost-Squares13:30 - Parts 10 and 100 and etc: The Beauty of Zooming Out19:40 - Part Infinity: ConclusionfinityThanks for watching! Leave a comment about your favorite part. And consider showing this video to a teacher in your life (if teachers incorporated more of these patterns when teaching arithmetic, I don’t think as many people would hate multiplication tables!).If you want bonus content, I've been doing livestreams every few days on my @Domotro channel, which are saved like videos on that channel's "live" tab afterwards. This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg, with some additional filming help from Raphael Matos and Andy Sykora. Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offutt, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! Check out the Combo Class Patreon at patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms, some topics mentioned in this episode include: times tables / multiplication tables, memorization vs. learning patterns, square numbers, almost-square numbers such as pronic numbers and numbers of the form n^2 - 1, graphs such as y=n/x, number factors, where numbers of different amounts of digits live on the times table, number theory, random fun math facts, a few arithmetic tricks, feeding some squirrels, and more!Disclaimer: Do NOT copy any dangerous-seeming actions (which were actually performed in a careful way) involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is an episode of a show that is purely meant to provide entertainment and education. Also, do not copy the squirrel-feeding without doing research, since if you feed wild squirrels in certain habitats, it will actually be bad for their diet and hunting skills in the long term.
The Truth About the Most Controversial Number Combo Class 2023-09-30 | For centuries, humans have argued about whether 0.999 (repeating) = 1, and there are still many misconceptions on BOTH sides of that debate. In this extra-long episode, I’ll take you on a journey through infinite decimals to help clear some things upMost of this episode is mathematical demonstrations, but there is also a philosophical edge to this topic, so leave a comment letting me know your personal opinions/beliefs about this "number" (hopefully after watching this whole episode to see all of the misconceptions I cover). And/or leave a comment if you can count how many squirrels appear in this episode haha.A few clarifications: -- For the definition of the Archimedean property, I accidentally spelled it Archimedian, and also I should have clarified that the numbers should be positive and that n should be an integer. -- I mentioned the commutative and associative properties just as recognizable examples of properties that humans take for granted about the real numbers, which can sometimes be lost when switching systems. They are not specifically the properties that are lost by the hyperreal or surreal systems I mentioned (if/when I make an episode about those systems in the future, I’ll clarify more about which properties become more difficult in those).-- When I said that every terminating decimal has two representations, I should have added "non-zero" since zero is technically terminating but doesn't have the same type of alternate form.-- Some comments thought that I shouldn't have used "controversial" as a description and claimed that nobody disagrees about this topic nowadays. Let's appreciate the irony of people arguing that nobody is arguing haha. If you look at the comments of this video, you can see that it's clearly still a topic many people disagree/debate about.Make sure you're also tuned in to my @Domotro channel for my livestreams, shorts, and other bonus content!This episode was filmed by Carlo Trappenberg, and was directed / edited / soundtracked by me (Domotro). Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offutt, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! Check out the Combo Class Patreon at patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms, some topics mentioned in this episode include: 0.9999999 (0.9 repeating / zero point infinite nines) and whether that = 1, repeating decimals, patterns in different numeral bases, what consists of a proof vs. a demonstration, properties of the real numbers such as the commutative and associative properties, the hyperreal and surreal numbers, infinitesimal numbers represented by epsilon, the philosophy of why numbers are useful, fractions vs. decimals, irrational numbers like pi, multiple representations of numbers in bases, and more...Disclaimer: Do NOT copy any dangerous-seeming actions (which were actually performed in a careful way) involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is for education and entertainment.
Clocks Are Designed Wrong, So I Created Better Alternatives Combo Class 2023-09-16 | 0:00 - Part A : Intro1:37 - Part I : Numerals6:06 - Part 0 : Zero12:39 - Part -1 : Negatives17:44 - Part 1/2 : Fractions20:01 - Part 55 : Equalization23:32 - Part Infinity : OutroIn this episode, we will explore some of my ideas of how the clock systems are poorly designed and how they could be fixed in the future. Leave a comment letting me know your favorite (or least favorite) of these ideas, or any of your own ideas!Make sure you're also tuned in to my @Domotro channel for my livestreams, shorts, and other bonus content!This episode was filmed by Carlo Trappenberg, and was directed / edited / soundtracked by me (Domotro). Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema! Check out the Combo Class Patreon at patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comDisclaimer: Do NOT copy any dangerous-seeming actions (which were actually performed in a careful way) involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is for education and entertainment.
The Fake Infinities in Math and Magic Cards Combo Class 2023-08-31 | Let's me show you some misconceptions about "infinity" vs. "arbitrarily large" things, by visiting blackberry patches, investigating prime numbers, and discussing "Magic cards"!0:00 - Part 1: Blackberries2:50 - Part 2: Prime Numbers12:42 - Part 3: Magic Cards23:45 - Part "Infinity": OutroMake sure you're also tuned in to my @Domotro channel for my livestreams, shorts, and other bonus content!This episode was filmed by Carlo Trappenberg, and was directed / edited / soundtracked by me (Domotro). Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, and Fredrik! Check out the Combo Class Patreon at patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms, topics discussed in this video include: infinity, arbitrarily large numbers/things, blackberries, prime numbers, arithmetic progressions, the Green-Tao theorem, Magic the Gathering cards, "infinite combos" vs. arbitrarily large combos, the "Combo Winters" of Urza's block and Mirrodin block, squirrels, and more!
Friendly Numbers and the Negative Level of the Divisor Function Combo Class 2023-08-18 | Let me tell you about "friendly numbers" and "solitary numbers". Along the way we will meet "multiperfect numbers", level -1 of the divisor function, a mystery about the number 10, and more!Here are some episodes about semi-related topics I've made in the past:About aliquot sums and fun nicknames - youtu.be/Cw0IYZuo3HUAbout how perfect numbers relate to primes - youtu.be/MoQqFDVo4cIMake sure you're also tuned in to my @Domotro channel for my livestreams, shorts, and other bonus content!This episode was filmed by Carlo Trappenberg, and was directed / edited / soundtracked by me (Domotro). Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, and Fredrik! Check out the Combo Class Patreon at patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case anybody searches any of these terms, topics discussed in this video include: the divisor function, sum of divisor function, sigma function, aliquot sums, factors/divisors, proper divisors, perfect numbers, multiperfect numbers, hemiperfect numbers, abundant numbers, deficient numbers, friendly numbers, solitary numbers, cats, squirrels, and lots of other cool things
10 Fruit Peels You Never Knew Were Edible Combo Class 2023-08-09 | In this episode, I explain the “edible peel conspiracy” by eating a lot of surprising things!(This just a “snack break” but is still an important and fun episode)Disclaimer: Do NOT copy any of the peel-eating you see me doing here (do your own research) or any uses of fire you might see here....We'll be back to another number theory topic next week. Sometimes it's important to have a little snack break, and sometimes a snack break ends up containing the seeds (or peels?) of a whole conspiracy...Make sure you're also tuned in to my @Domotro channel for my livestreams and other bonus content!This episode was filmed by Carlo Trappenberg (who also has a cameo in it). It was directed/edited/soundtracked by me (Domotro). Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, and Fredrik! Check out the Combo Class Patreon at patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com
The Collatz Conjecture... but in Binary Combo Class 2023-07-31 | Let me explain the “3x+1” mystery (the Collatz conjecture) and show some cool shortcuts that happen if we interpret it in binary, as well as some extensions like including negative numbers! Make sure you're also tuned in to my @Domotro channel for my livestreams and other bonus content!This episode was filmed by Carlo Trappenberg (plus a few scenes filmed by Jonathan Ruchlis). It was directed and edited by me (Domotro) and I also made the music in the soundtracks. And here's a link to the public domain fractal image I included near the end: en.wikipedia.org/wiki/Collatz_conjecture#/media/File:CollatzFractal.pngA small correction: near the end, when showing the negative number patterns, I had 1-2-4 written above those as an example of the positive loop, but 1-2-4 is in backwards order with the way I drew the arrows (arrows+error=errows?). That was meant to refer to the normal 4-2-1 loop (which could also be written as 1-4-2 or as 2-1-4) that was in the earlier portions of the episode.... There's also a few little typos: I misspelled "result" as "resut" one one whiteboard, and I accidentally typed "and my" twice on one of the credits whiteboards. Whoops. Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, and Fredrik!... (Also thanks to my cats Sage, Dandelion, and Sassafras! Can you spot all 4 of Dandelion's catmeo appearances in this episode?) Check out the Combo Class Patreon at patreon.com/comboclassIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comDISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
Fermats Last Theorem and the Mysteries That Remain Combo Class 2023-07-22 | In this episode, first I'll explain the historical tale of Fermat's Last Theorem, and then show some other mysterious questions, including a conjecture Euler got wrong and the unsolved $1,000,000 "Beal conjecture"![Disclaimer: Do not copy any uses of fire that you may see in this episode]. Here's my previous episode about Pythagorean triples: youtu.be/wtONmrYQaQUMake sure you're also tuned in to my livestreams and other bonus content on my @Domotro channel!This was filmed by Carlo Trappenberg.Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, que and George Sharabidze!--------------------------To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclassSupporting me there helps allow the channel to improve, and also helps prevent me from needing to put any sponsored ad segments within these episodes (I have turned down sponsorships from companies who would have paid me to advertise a product during these episodes).If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these terms, some of the topics discussed in this episode are: Pythagorean triples, Pierre de Fermat, Fermat's Last Theorem, Euler's Sum of Powers Conjecture and similar questions in number theory, the Beal conjecture, Andrew Wiles, and much more!DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
Pythagorean Triples (and Quadruples) Are Everywhere! Combo Class 2023-07-09 | In this episode, I’ll show some cool ways “Pythagorean triples” are hiding all over geometry, and then discuss the underrated “Pythagorean quadruples”!This episode about Pythagorean triples/quadruples is the first part of a 2-episode arc. Next episode (coming in a week) will continue this topic into Fermat's Last Theorem and beyond. I love you all, thanks for watching. Also make sure to check out my @Domotro channel if you want to see my bonus content like livestreams (and other links in this video description).Leave a comment with your favorite animal cameo in this video (there's a squirrel carrying a nut, some cute cats, and some cool bird noises).This was filmed by Carlo Trappenberg.Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, and Brooks Boutwell!--------------------------To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclassSupporting me there helps allow the channel to improve, and also helps prevent me from needing to put any sponsored ad segments within these episodes (I have turned down sponsorships from companies who would have paid me to advertise a product during these episodes).If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these terms, some of the topics discussed in this episode are: Pythagorean triples, Pythagorean quadruples (and Pythagorean quintuples and beyond), the Pythagorean formula (a squared plus b squared equals c squared), right triangles, circles and spheres, squares and rectangles, gridpoints with integer coordinates on a coordinate plane, points on the unit circle with rational coordinates, other geometric analogies, and more. (There's also some cool cats and squirrels in this video haha).DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
The Secret Cycles in the Fibonacci Sequence Combo Class 2023-06-22 | Let me show you how the Fibonacci sequence has some cool patterns hiding within its last digits, and how this relates to other patterns it would have if we counted in different bases! Here's a previous episode explaining more about how different "mods" work: youtu.be/hH89nUGd6DUHere's a previous episode showing some cool links the Fibonacci sequence has with the "golden ratio": youtu.be/cmziKiMmfl4I called this "secret" in the title because many people who know the Fibonacci sequence have never heard about this awesome hidden layer to it. However, to a number theorist, it's not a "secret", and you can look up "Pisano periods" if you want to find a lot more research that has been done about this topic.Clarification: on the title cards at about 12 minutes, when I say 2 fibonacci numbers in a row that are the "same" last digit, I don't mean the two numbers in the pair have to be the same as each other, I mean that the pair has to be the same as a previous pair we've seen before.I've been posting some "shorts" on this channel (6 so far) without sending them to subscriptions/notification feeds, so check those out here: youtube.com/@ComboClass/shortsAlso make sure you're tuned in to my @Domotro channel where I post bonus math videos and livestreams and stuff!This was filmed by Carlo Trappenberg.Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, and Jan Bosenberg!--------------------------To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass... Supporting me there helps make the channel improve, and also helps prevent me from needing to put any sponsored ad segments within these episodes (I have turned down sponsorships from companies who would have paid me to advertise a product during these episodes).If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these terms, some of the topics discussed in this episode are: the Fibonacci sequence / Fibonacci numbers, modular arithmetic, the "Pisano periods" of the Fibonacci sequence for various different mods and its cycles related to powers of ten, how "last digits" of a number relate to its representations in different bases and different mods, etc...If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
Mathematicians Just Discovered These Shapes! Combo Class 2023-06-13 | A few months ago, mathematicians discovered the first "aperiodic monotile", and in the weeks since then, they've discovered new and improved families of these shapes. Let me tell you about the history of aperiodic tilings, from “Penrose tiles” to the “hat" monotile to the newest “spectre" monotiles that were just discovered! Some clarifications/corrections:- In the example I gave at 5 minutes, I used squares (which I thought was more unique than the more common examples that use rectangles) but I should have used rectangles, as I realized afterwards that shifting columns of a square grid wouldn't be quite enough to make it not periodic in all directions. The overall point there, that many periodic tilings can be altered to create non-periodic tilings, is true.- When I describe how some tilings have a "glitch" but then have an arbitrarily large section that can be translated onto a matching section, some sources would call that tiling non-periodic due to the glitch. I should have called that type "not aperiodic" as opposed to "periodic" to be clearer. It's true that it still wouldn't be "aperiodic" (a different term than when sources say "non-periodic") if it had an arbitrarily large section that can do that.I've been posting some "shorts" on this channel (6 so far) without sending them to subscriptions/notification feeds, so check those out here: youtube.com/@ComboClass/shortsAlso make sure you're tuned in to my @Domotro channel where I post a bunch of bonus math videos, and also do livestreams a couple days a week!One of those livestreams was right after the most recent monotile discovery came out, and contains another description of aperiodic tilings and a look through the papers I'm referencing: youtube.com/live/u8WifFDQ6yQ?feature=shareHere are the two papers published this year with the new discoveries:arxiv.org/abs/2303.10798arxiv.org/abs/2305.17743In this video, I used some images from those two papers, as well as some images from Wolfram “Mathworld” (images created by Eric W. Weisstein) and Wikipedia (images contributed by the users Maksim, Inductiveload, Parcly Taxel, and Geometry Guy).This was filmed by Carlo Trappenberg.Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, and Julian Zassenhaus.--------------------------To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass... Supporting me there helps make the channel improve, and also helps prevent me from needing to put any sponsored ad segments within these episodes (I have turned down sponsorships from companies who would have paid me to advertise a product during these episodes).If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these terms, some of the topics discussed in this episode are: 2D tilings/tesselations, periodic tilings, aperiodic tilings, squares / triangles / pentagons / hexagons, Wang tiles / Wang dominoes, Penrose tiles (including the "kite" and "dart" shapes), the new "hat" aperiodic monotile discovered by David Smith, the even newer "spectre" tiles that are chiral aperiodic monotiles he discovered, and more!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
The Mystery of the Unknown Ramsey Numbers Combo Class 2023-06-02 | Let me explain about "Ramsey numbers", an interesting unsolved mystery with recent mathematical progress, which we can visualize through colorful shapes and analogies about parties!Also, here are a few bonus "shorts" I released since last episode (I didn't send them to notifications or subscription feeds, so you may not have seen them)youtube.com/shorts/dSDUvl14ZLo?feature=shareyoutube.com/shorts/vqBB1FkbcEo?feature=shareAlso make sure you're tuned in to my @Domotro channel for my bonus videos, livestreams, and other content!This was filmed by Carlo Trappenberg.Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, and Julian Zassenhaus.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass)If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these terms, some of the topics discussed in this episode are: Ramsey numbers (especially "diagonal Ramsey numbers") such as R(5,5), Ramsey's theorem / Ramsey theory, Graham's number, graph theory, complete graphs, the analogy sometimes called the "theorem on friends and strangers", the mathematician Paul Erdos, aliens, computers, and lots more!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
The Amazing Mathematics of the Golden Ratio Combo Class 2023-05-23 | Let me show you some awesome numerical patterns within "the golden ratio", beginning with a story about this number from my childhood, and building to a whole web of connections it has with the "Fibonacci sequence", the "Lucas numbers", and more! Many people associate this number/ratio with geometry and shapes, but there are tons of numerical traits that make it special too! This episode covers some of my favorite numerical aspects and doesn't cover the geometric aspects, which I will cover at another point in the future. The golden ratio will also play a key role in a future episode about irrational numbers. And in another future episode, we will meet some other "metallic" numbers such as the "silver ratio" and "bronze ratio"!By the way, the symbol I am using for the golden ratio is the greek letter "phi", which is used for a few things in math, one of which is this number. "Phi" is pronounced more like "fee" according to the sources I've read, although you'll hear some people pronounce it like "fye".Here's links to two previous episodes that include the Golden Ratio: youtu.be/hI-pwt7LyUwyoutu.be/YCJ99liapCQ(doesn't matter if you watch these before or after this video)Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, and Julian Zassenhaus.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass)Make sure you're also tuned in to my @Domotro channel for my bonus videos and livestreams and other content!By the way, I've started putting shorts on this channel but they typically won't go to notifications or subscription feeds (they typically have been on my @Domotro channel and did so well for that channel that I want more people on that shorts page to find this channel too). They will be available on the "shorts" tab on this channel, and I will link the recent ones in video descriptions like this. Here are the ones I've put on this channel so far:youtube.com/shorts/vqBB1FkbcEo?feature=shareyoutube.com/shorts/Hk6sE9-M1mA?feature=shareyoutube.com/shorts/blqO-RaKrMI?feature=shareyoutube.com/shorts/zhOiUNQtGF4?feature=shareIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these words, some topics mentioned in this video are: the golden ratio (phi), square numbers, cube numbers, other integer powers, the fibonacci sequence, the lucas numbers, infinite continued fractions, infinite square roots, and more!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
How to Easily Identify Any 2-Digit Prime Number Combo Class 2023-05-16 | Let me show you some techniques and shortcuts that will let you easily identify whether any number under 120 is a prime number or not. Along the way, I’ll also show some symmetrical patterns within composite numbers, rectangles, and square roots! I noticed a little problem with the version of this I uploaded a few hours ago, so I took that down and here’s the fixed version. Hope you all enjoy!Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, and Julian Zassenhaus.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass)By the way, I've started putting shorts on this channel but they typically won't go to notifications or subscription feeds (they typically have been on my @Domotro channel and did so well for that channel that I want more people on that shorts page to find this channel too). They will be available on the "shorts" tab on this channel, and I will link the recent ones in video descriptions like this. Here are the two I've put on this channel so far: Here's the newest one: youtube.com/shorts/Hk6sE9-M1mA?feature=share Here's one about a geometric representation of the "difference of squares" identity: youtube.com/shorts/blqO-RaKrMI?feature=share Here's one about the difference between 1/0 and 0/0: youtube.com/shorts/zhOiUNQtGF4?feature=shareIf you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these words, some topics mentioned in this video are: prime numbers, composite numbers, factors, rectangles, square numbers, square roots, symmetry, and more!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
The Base Some Computers Use Instead of Binary Combo Class 2023-05-08 | Most computers use binary, but some actually use a lesser-known base called "balanced ternary". Let me show you how that cool base works, starting with some puzzles and building up to some awesome mathematical abilities that "balanced" bases have! (see below for links to the other videos I've made about different bases) To clarify a few things people asked about in the comments:-- Some people in the comments seem offended about the laptop destruction. That was not a functional computer. I would have needed to dispose of it in any case. I just had fun using it as a prop first.-- Yes, ternary computers have actually been made before! For example, some were manufactured by the Soviet Union in the past. They have never been as widespread as binary computers, but you never know what the future may hold!-- In the weighing puzzle, by "test" the weight of a target item, I mean that you have to find a way to "equal" the item's exact weight (as if figuring out that it is a particular weight and confirming it is precisely that)Here are some previous episodes I've made about different bases: How to Count in Base Negative 10 - youtu.be/GWA_NraxOUw How to Count in Fractional and Irrational Bases - youtube.com/watch?v=hI-pwt7LyUw How to Count in Base 2i - youtu.be/MM0Sbfvf2Hw Patterns Across the "Basic" Bases: youtu.be/qa8GuQLB7WkBy the way, I've started putting shorts on this channel but they typically won't go to notifications or subscription feeds (they typically have been on my @Domotro channel and did so well for that channel that I want more people on that shorts page to find this channel too). They will be available on the "shorts" tab on this channel, and I will link the recent ones in video descriptions like this. Here are the two I've put on this channel so far: Here's the newest one: youtube.com/shorts/Hk6sE9-M1mA?feature=share Here's one about a geometric representation of the "difference of squares" identity: youtube.com/shorts/blqO-RaKrMI?feature=share Here's one about the difference between 1/0 and 0/0: youtube.com/shorts/zhOiUNQtGF4?feature=shareSpecial thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, and Julian Zassenhaus.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass)If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these words, some topics mentioned in this video are: balanced base 3 (balanced ternary), weighing puzzles that encode numeral bases, other balanced bases, symmetry, truncating numbers vs. rounding numbers, a possibility for a ternary currency system, the powers of 3, threevens vs. throdds, the mathematician donald knuth, how and why most computers use binary compared to some computers that use balanced ternary, and more!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
The Hidden Hexagons Inside Bananas Combo Class 2023-05-01 | What does a banana have in common with a beehive? Maybe more than you realize! Join me for a combo of a snack break and a math lesson about polygons/tilings, where I'll show you some interesting mathematical things I realized about bananas this week!To note: many bananas (although not all) evolved from "triploid" genes which relate to the 3's in their structure. However, that doesn't end the story, because in an alternate timeline, triploid genes might have never successfully evolved banana-like fruits whereas a banana-like fruit might have evolved from a different genetic source. What traits make the 3-structure functional enough to have evolved into such a common fruit and maintained that shape over years of natural selection, while some other genetic structures never managed to successfully evolve a banana-like fruit? In this video I explore some of that.Announcement: Hope you all had a happy April! I'll hopefully have a new episode out on this channel every weekend in May. I also have begun releasing some "shorts" on this channel (which I used to only post on my @Domotro channel) but I will not currently be having them alert notifications or subscription feeds in the way that these full episodes do, so it won't bother viewers who only want to see full episodes. They are mostly for the purpose of introducing this channel to more people on the shorts page, since the Grade -1 shorts I posted on my @Domotro channel were surprisingly successful at showing that channel to more people (and now it has way more subscribers than this "main" channel). The main focus of this channel will always still be the full episodes.... If you do want to keep up to date with the shorts on this channel, I will try to link any new ones in the descriptions of my new full episodes like this, so you can check these descriptions if you care. Here's the first short I've put out here so far, about the difference between 1/0 and 0/0: youtube.com/shorts/zhOiUNQtGF4?feature=shareSpecial thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, and Claudio Fanelli.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass)Additional thanks to "TravelingThroughTime" (who mailed me the wasp nest I showed in this video), and to George Carozzi (who mailed me some cool science/math toys, including some that are visible on my desk in this episode).If YOU want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these words, some topics mentioned in this video are: bananas, beehives, equilateral triangles, squares, regular pentagons, regular hexagons, other regular (convex) polygons, formulas for total angles and interior angles in regular polygons, triangular tilings/grids, square tilings/grids, hexagonal tilings/grids, and more!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)By the way, I try not to waste food, so after filming this episode I ate a LOT of bananas haha.DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
The Unusual Mathematics of Modular Division Combo Class 2023-04-25 | In the land of "mod 60" (which works like minutes on a clock) "1 divided by 7" is 43, while "1 divided by 6" is impossible! Let me show you the strange patterns of "modular division", a deep mathematical concept which we can visualize through clocks and calendars....I had hoped to have this episode out a couple days ago, but my computer broke over the weekend. I got a new one, but had to re-edit this episode. Now things should be back on track with another new episode this weekend. And make sure you're also subscribed to my @Domotro channel which has lots of shorts, livestreams, and bonus videos in between the main episodes here.Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, and Michael Friemann.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass)Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you have any extra clocks/dice/etc. that you'd like to see in the background of Grade -2, here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these words, some topics mentioned in this video are: clock math, modular arithmetic (particularly mod 60 and mod 7), modular addition, modular subtraction, modular multiplication, modular division, coprime (also known as relatively prime) numbers, which operations have the property of being "closed" in which realms of numbers, and more!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
Extending Prime Factorizations Beyond Whole Numbers Combo Class 2023-04-16 | The common definition of “prime factorization” should be changed! Schools often teach about this concept without ever revealing any of the cool extensions that allow it to unlock larger realms of numbers. Let me take you on a journey to explore the TRUE potentials of prime factorizations!Make sure you're also subscribed to my @Domotro channel which has lots of shorts, livestreams, and bonus videos in between the main episodes here. The next main episode on this channel will be coming out about a week after this one.Here are some chapters (although I hope most of you watch the whole episode)0:00 - What are prime factorizations?0:49 - Which properties do we want to preserve?2:49 - Can we extend the primes?6:45 - Can we extend the exponents?10:58 - Should we change the definition?13:16 - Can we make further extensions?Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Beugul, OmegaRogue, Florian, William Hawkes, and Michael Friemann.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass) Some notes about this episode: I kind of phrased this episode as “most people don’t know about this main extension to prime factorizations”, but I'm sure some of you already do. If that’s you, awesome, you must have had a good teacher or other resource (and still watch this whole episode since I include various other mathematical ideas and ways to take it even further). However, a surprising amount of people don't know about this, and I think this main "extension" should be taught much more commonly and earlier, and be a more common part of the usual definition that prime factorizations are “defined” as in most schools and textbooks. As for the further extensions I mentioned near the end, I'll probably continue that thought process in a later episode (leave a comment if you have any thoughts/ideas about any of this). To clarify about the "goal" of these different "levels": I was just analyzing ways we could "add" to the current rules at each stage, without losing any numbers that were previously allowed, but some commenters pointed out that you might also be able to change the base numbers in other ways (and preserve the one-to-one property) if you incorporated certain systems like quadratic extensions or complex number factorizations that change what it means to be "prime" (and would exclude some prime numbers from being included as base numbers and thus prevent some double representations from occurring). I'll have to ponder that more, and yes, I'll explain more about those systems in a future episode. In this episode, I was assuming that we were keeping all of the typical primes as possible base numbers in the prime factorizations, while just attempting to add new options. This episode was experimental, though, so feel free to comment your own opinions!Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you have any extra clocks/dice/etc. that you'd like to see in the background of Grade -2, here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)comIn case people search any of these words, some topics mentioned in this video are: prime factorizations, positive and negative integers, fractions, the number 0, rational numbers, irrational numbers, the golden ratio, square roots, cube roots, prime numbers, imaginary numbers, negative exponents, fractional exponents, and more!By the way, near the beginning of this episode, there's a cool moment where two squirrels run by in a row!If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.
Welcome to Grade -2 of Combo Class! Combo Class 2023-04-08 | This is the beginning of Grade -2.... A longer mathematical episode will be coming out next weekend. In the meantime, check out my @Domotro channel and also make sure you've seen the Grade -1 finale: youtu.be/RLhNlK-MUHgDISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this video or series. This is for educational (and entertainment) purposes.Full math episodes will return next week, and I'll have a new episode out here every weekend for the rest of April (and after that there will often be 1 per week but sometimes up to 2 weeks between longer ones). Like last grade, many episodes will be focused on math (in particular, "number theory" will get a lot of focus), but there will also be episodes about other topics (such as language and science). During this grade, I will also occasionally be posting my favorite of the new "shorts" I make (which usually go on my @Domotro channel) on this channel instead, since Youtube's shorts page has done a remarkable job at introducing new viewers to that other channel, and I want more people to find this channel too. Don't worry, those won't ever become the main focus here, and making full episodes is still my main goal. The majority of my "shorts" (as well as my other more casual content such as bonus lessons and livestreams) will still be going on that @Domotro channel.Special thanks to Evan Clark and to all of my Patreon supporters:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Beugul, OmegaRogue, Florian, and William Hawkes.(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at patreon.com/comboclass)Come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you have any extra clocks/dice/etc. that you'd like to see in the background of Grade -2, here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com
The Grade -1 Finale Combo Class 2023-04-01 | This is the Grade -1 finale. It's a documentary about how I created Combo Class during the past year (while getting two surgeries) and also includes a bunch of new adventures as a transition into Grade -2. This is the longest episode yet and the most personal video I've ever released. I added timestamps of different chapters, but please consider watching the whole thing as a short film. DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this video. This is for educational (and entertainment) purposes.The first official episode of Grade -2 will come out on this channel in a week or two (which will just be an introductory welcome with some fun surprises, but the mathematical number-related videos will also return later in April!). In the meantime, there will be bonus content on my @Domotro channel. By that way, that channel is newer than this channel, but actually has way more subscribers than this one due to all the shorts I've posted there. Youtube is sending me one of those silver play button award things in the mail for passing 100K subscribers there, which is a super crazy and awesome thing to happen within our first (negative) grade!Chapters:0:00 - Introduction0:55 - First Half of Haircut2:21 - Videos I Made Before Combo Class5:20 - The Issues and Injuries I Had8:32 - Burning the First Clock10:18 - The Surgeries I Got Last Year13:31 - Recurring Symbols16:48 - Taking a Field Trip18:55 - Classroom Camping22:03 - Fires and Floods24:11 - Updating the Class Rules26:47 - Special Thanks Section30:26 - Labcoat Upgrade31:27 - Second Half of Haircut32:51 - Grade -2 CluesAlthough I added chapters, please consider watching the whole thing like a short movie. If you enjoyed it, leave a comment with your favorite part! (Also I hid some secret clues in this video. Do you see them?)To help support Combo Class and get some cool bonus content, check out my Patreon at: patreon.com/comboclass (in the special thanks section of this video, I list the names of all the people who have supported through there so far). You can also come chat with other combo lords on the Discord server here: discord.gg/cHHvDcPPucand there is a subreddit here: reddit.com/r/comboClassIf you have any extra clocks/dice/etc. that you'd like to see in the background of Grade -2, here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com
I Hate Tests... So I Created One Combo Class 2023-03-13 | In this video, I present the unique "Grade -1 final exam" (consisting of a mathematics section and then two other rare sections). Even if you don't like tests, this will be a fun video, trust me. If you end up wanting to try part of this "test", the text version of it is linked below. (Don't comment any of the "answers" here anless you mark it as a spoiler in the way I describe below!)The text version of this test is available here as a Google document:docs.google.com/document/d/1KT0kogPPateH4aeKit_EKjtKf6ABdTDYe9qATaEiwmo/edit?usp=sharingI'll also post it on the Discord here: discord.gg/cHHvDcPPucIf you try any parts of this test, let me know in a comment! However, this exam is meant as an optional personal challenge for each of you, so try not to spoil the answers of the math section for each other (which will be officially released in a video on my @Domotro channel in a week). If you want to comment any answers, please put "spoiler" on top and leave a bunch of lines of extra space so people would need to click "read more" to see. Sorry but I will remove comments if they contain spoilers right at the top! (You can also comment answers marked as spoilers in the Discord in the "puzzle discussion" thread).Stay tuned for a long Grade -1 finale/documentary episode coming later in March (the first scene of which I posted on Patreon for my supporters there), and then Grade -2 coming in early April.... In the meantime, there will be bonus content on my @Domotro channel (WHICH JUST PASSED 100K SUBSCRIBERS) including weekly livestreams I'll be doing the rest of March on every Monday at 10 AM Pacific Time, and every Thursday at 6 PM Pacific Time.Check out my Patreon at patreon.com/comboclass if you want to support the channel, get some cool bonus content, and get your name on a whiteboard in the Grade -1 finale! Thanks to all of my supporters there:Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Beugul, and OmegaRogue.If you have any extra clocks/dice/etc., here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: youtu.be/_-gSvbvO8W4Domotro1442 A Walnut Street, Box # 401 Berkeley, CA 94709Also check out the subreddit at reddit.com/r/comboClassSome topics in this video include: school tests, IQ tests, personality tests, problem solving, even numbers, threeven numbers, clocks, modular arithmetic, writing numbers in different bases, square numbers, factorials, platonic solids, dice, natural density, prime signatures, factors, tetration, roots of unity, various "number theory" concepts, opinions, language, plants, animals, appreciation, love, and more!. I also show some exaDISCLAIMER: never try to copy any physical actions you see in Combo Class, such as anything involving fire, tools, science experiments, or falling clocks.
The Land Between Numbers and Letters Combo Class 2023-03-03 | Let me show you a bunch of cool patterns within the words we use for numbers in English, and some surprising traits that show up when numbers are given names in a language!Next episode (coming out on March 12th) is the 2nd last episode of Grade -1, and will be my unique version of a "final exam" (it will be a fun video even for people who hate tests). If anybody wants to "study" for the exam, you can rewatch older episodes on this channel (most of the questions will require a mix of some knowledge from one of my episodes and some problem-solving and/or basic arithmetic from you). After that, later in March, will be the Grade -1 finale, which will be like a documentary about making this crazy grade and transitioning to Grade -2.During March I will be livestreaming on my @Domotro channel every Monday at 10 AM Pacific Time, and every Thursday (except March 2nd) at 6 PM Pacific Time, so stop by some of those if you want to see some fun random activities and/or ask me anything in the chat. (They also will be timestamped with chapters afterwards for people who can't watch them live).Check out my Patreon at patreon.com/comboclass if you want to support the channel, get some cool bonus content, and get your name on a whiteboard in the Grade -1 finale! Thanks to all of my supporters there:George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Beugul.If you use Discord, join us on the Combo Class channel where there are lots of fun conversations going on: discord.gg/cHHvDcPPucThere's also a subreddit at reddit.com/r/comboClassAnd make sure you're also subscribed to my other channel @Domotro for my shorts, livestreams, and bonus videos.[Some topics mentioned in this episode include: words for numbers, the English language, the long scale vs. short scale for numbers like one million and one billion, a number naming system invented by John Conway and Richard Guy and written about in the book "The Book of Numbers", what's special about four, what's special about eight and zero, what's special about one and forty, rare number words that have all their letters in alphabetical order, what happens if we alphabetize all of the numbers compared to each other, and other crazy things in the land between language and math]DISCLAIMER: never try to copy any physical actions you see in Combo Class, such as anything involving fire, tools, science experiments, or falling clocks.
Base 1010 and the Realm of Number Representations Combo Class 2023-02-23 | Outside our typical way of viewing numbers, there's a whole realm of different representations each number has. Follow me into this realm to see a bunch of awesome patterns that not enough people know about! Do you have any old clocks or other items you'd like to see in the background of my future videos? Well, like I mentioned at the end of this episode, I have a new private mailbox where you can send things! If you might want to send anything, watch this short video on my @Domotro channel which contains some brief guidelines and the mailbox address: youtu.be/_-gSvbvO8W4By the way, to clarify: in this episode, I’m using the word “numbers” to mean base-independent amounts of things (and only positive integer amounts, along with sometimes zero), and I'm using the word “representations” to mean the strings of digits that can express numbers in different bases. For the type of bases that I was discussing (positional numeral systems based on powers of an integer larger than 1), I nicknamed them "basic bases", which is a term I might continue using in the future, since there are many patterns you can say are true for "all basic bases", but which might not hold for "all bases" in general if you include things like tally marks or some of the more obscure bases I've covered in past episodes.I didn't put any background music in this episode like I usually do, because there were a bunch of birds making nice sounds in the background the day I filmed this, and I wanted to let you appreciate the Combo Classroom's natural soundscape for a bit!If you enjoy this episode, make sure you've checked out these other episodes on my channel about some rarer types of number bases: How to Count in Base Negative 10 - youtu.be/GWA_NraxOUw How to Count in Fractional and Irrational Bases - youtu.be/hI-pwt7LyUw How to Count in Base 2i - youtu.be/MM0Sbfvf2Hw Also here's my episode about "highly composite numbers" - youtu.be/cV0Y0Ay3ev4 And here's one of my episodes about "modular arithmetic" - youtu.be/hH89nUGd6DUCheck out my Patreon at patreon.com/comboclass if you want to support the channel, get some cool bonus content, and get your name on a whiteboard in the Grade -1 finale! Thanks to all of my supporters there:George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Beugul.If you use Discord, join us on the Combo Class channel where there are lots of fun conversations going on: discord.gg/cHHvDcPPucThere's also a subreddit at reddit.com/r/comboClassAnd make sure you're also subscribed to my other channel @Domotro for my shorts, livestreams, and bonus videos.[Some topics mentioned in this episode include: positional numeral bases, bases that consider themselves to be called “Base 10”, the last digit of numbers in different bases, what it means to end in a 0, prime numbers, highly composite numbers, square numbers, cube numbers, perfect powers, factors/divisors, modular arithmetic, and more!]DISCLAIMER: never try to copy any physical actions you see in Combo Class, such as anything involving fire, tools, science experiments, or falling clocks.
The Pandigital Paradox Combo Class 2023-02-05 | "Pandigital numbers" (numbers that contain every digit) might seem random, but let me show you how important and mysterious they truly are. Prepare for pandigital pandemonium, including primes, palindromes, perfect powers, and paradoxical truths about numbers. This is the longest episode on this channel yet and is full of surprises (leave a comment if you see all 3 squirrel cameos!).[DISCLAIMER: DO NOT COPY ANY OF THE PARTS WITH FIRE. In general, never copy any physical actions you see in Combo Class, such as anything involving fire, tools, or other science experiments.]For more details about some of these topics, check out:My episode about factorials - youtu.be/b2zhTrggRDEMy episode about palindromic numbers - youtu.be/qEk99UzFPZUMy episode about “hyperelevens” - youtu.be/MoQqFDVo4cIMy latest two livestreams on my bonus channel:(the one before this episode) - www.youtube.com/watch?v=AecFu0bU-pQ(the one after this episode) - youtu.be/2dWsycRKf0ASpecial thanks to my Patreon supporters: Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Max.Combo Class Links:Patreon: patreon.com/comboclassDomotro bonus channel: www.youtube.com/@domotroReddit: reddit.com/r/comboClassDiscord: discord.gg/cHHvDcPPucSome of the topics in this episode include: pandigital numbers and zeroless pandigital numbers, pandigital prime numbers, pandigital perfect powers such as square numbers, pandigitally “persistent” numbers, “polydivisible” numbers, palindromic numbers, hyperelevens (often referred to as “generalized repunits”), pandigital numbers in other bases like Base 2 (binary), Mersenne primes (the biggest primes ever discovered), ways to compare sizes of infinite things such as “natural density”, and some paradoxical traits about pandigital numbers that I realized when investigating them!
How to Count in Base 2i Combo Class 2023-01-24 | Let me show you the mysterious powers of Base 2i (and other interesting bases you've probably never heard of).Links to my episodes about negative bases and irrational bases:How to Count in Base Negative 10 - youtu.be/GWA_NraxOUwHow to Count in Fractional and Irrational Bases - youtu.be/hI-pwt7LyUwSpecial thanks to Evan Clark, and to my Patreon supporters: Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Max.Combo Class Links:Patreon: patreon.com/comboclassDomotro bonus channel: www.youtube.com/@domotroReddit: reddit.com/r/comboClassDiscord: discord.gg/cHHvDcPPucThis episode is about the strange mathematical and philosophical potentials of imaginary and complex positional numeral bases, and what they can achieve within the complex numbers and the "Gaussian integers". It mostly focuses on Base 2i, also known as the "quater-imaginary base" (original written about by Donald Knuth). We will also discuss the "Base i-1" (a.k.a. Base -1+i)" and "Base -i-1" (a.k.a Base -1-i) systems, and how they relate to a cool fractal shape. We'll also look at the similarities (and differences) between these ways of counting and other possible bases such as negative bases, square root bases, and more!If you're reading this, leave a comment with which base is your favorite!Disclaimer: Do not copy any physical actions you see in Combo Class episodes, including any use of fire, tools, or other science experiments.
The Calendar With 13 Friday the 13ths Every Year Combo Class 2023-01-13 | Happy “Friday the 13th”! Let me show you a bunch of interesting things about calendars, including a roast of the current calendar system, a better calendar with 13 months, an explanation about "Leap Seconds", and a variety of other fun facts! To help support these videos and see behind-the-scenes content like the full uncut footage of the campfire scene from this, check out my Patreon at patreon.com/comboclass (and see below in this description for the names of my awesome supporters!)CORRECTION: Around the middle of the episode, I accidentally wrote/said (5) and (71) as the prime factorization of 365, but it's supposed to be (5) and (73). All appearances of "71" there should be "73".Stay tuned for an episode about how to count complex numbers in Base 2i (and Base i - 1) coming later in January. In the meantime, check out the Combo Class Bonus channel @Domotro for my short videos, bonus lessons, and livestreams!Some of the calendar topics discussed in this episode include: the phobia of the number 13 (known as triskaidekaphobia) and the more specific phobia of Friday the 13ths (known as paraskevidekatriaphobia or friggatriskaidekaphobia), the Gregorian Calendar, problems with February, ways to remember which months have 30/31 days, how Leap Days and Leap Seconds actually work, the 13-month "International Fixed Calendar", a possible 360-day calendar, my flooded classroom, how to cook an egg on a campfire, and more.Special thanks to my Patreon supporters: Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, and Izeck.Patreon: patreon.com/comboclassBonus channel: www.youtube.com/@domotroReddit: reddit.com/r/comboClassDiscord: discord.gg/cHHvDcPPucIf you're reading this, leave a comment with which calendar is your favorite!Disclaimer: Do not copy any physical actions you see in Combo Class episodes, including any use of fire, tools, or other science experiments.
The Scientific Shape of Bubbles (and Raindrops) Combo Class 2023-01-08 | Here’s a science break where I explain some interesting facts about raindrops and bubbles, then do fun experiments with homemade bubbles, bubbles-in-bubbles, and bubble machines (and my classroom floods!). Special thanks to my Patreon supporters at patreon.com/comboclass - top supporters are listed in this video’s credits, and all supporters are listed below.Next week on Friday the 13th will be a cool episode about calendars, and then the Base 2i episode will be coming later this month. Special thanks to: Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, and Stan Seibert.This episode was mostly filmed by Carlo Trappenberg (who has a cameo in it) and Domotro, but the end scene with the bubbles-in-bubbles was filmed by Solomon Zucker.COMBO CLASS LINKS:Patreon: patreon.com/comboclassBonus channel: www.youtube.com/@domotroReddit: reddit.com/r/comboClassDiscord: discord.gg/cHHvDcPPucIf you're reading this, leave a comment about which other bubble experiments you want me to try someday in the future!Disclaimer: Do not copy any physical actions you see in Combo Class episodes, including any use of fire, tools, or other science experiments.
A Clock Formula That Detects if a Number is Prime Combo Class 2023-01-03 | It's a new year, but there are still a few more months in Grade -1. In this episode, I'll use clocks to explain an interesting formula that can test whether any number is prime or composite. Special thanks to my Patreon supporters at patreon.com/comboclass (top tier supporters are listed in this video's credits and all supporters are listed below)After you watch this video, check out my bonus video about shortcuts for testing prime numbers if you were doing it yourself with a calculator: youtu.be/dl7LLYw-xbQSpecial thanks to: Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, and Stan Seibert.Disclaimer: Do not copy any physical actions you see in Combo Class episodes, including any use of fire, tools, or other science experiments.COMBO CLASS LINKS:Patreon: patreon.com/comboclassBonus channel: www.youtube.com/@domotroReddit: reddit.com/r/comboClassDiscord: discord.gg/cHHvDcPPucSome topics mentioned in this video include: prime numbers, factorials, clocks, modular arithmetic congruences, divisibility/remainders, Wilson’s theorem, Wilson primes, and more.Stay tuned for next episode, which is a more casual science break where I do some bubble experiments and the rain makes my classroom flood.If you're reading this, leave a comment about clocks.
