The Amazing Math behind Colors! @Kuvina

Kuvina Saydaki In this video, I talk about the math and science of colors for 42 minutes. Topics include cone cell response functions, electromagnetic radiation, spectral colors, luminance, color spaces, parametric equations, normal curves, mono and polychromatic light, emission spectra, spectral power distributions, chromaticity diagrams, linear transformations, the physics of diffuse reflection and light sources, blackbody radiation, sunlight, refraction, rainbows, rayleigh scattering, fluorescence, LEDs, color gamuts, CRT TV, LCD screens, CMYK printers, the RGB cube, binary, hexadecimal codes, the HSV color space, cylinder and cone, and color schemes. This is my entry in #SoME2

Corrections/Clarifications:
37:10 I misspoke and said m1 instead of m2. What is shown on screen is correct.
22:12 On screen it says λ = f/c, but this is wrong. The correct formula is λ = c/f
I have been told by some commenters that the long cone responsivity graph has a smaller, secondary peak, in the shorter wavelengths, and this is a reason why monochromatic violet appears more red than a pure blue. I have found conflicting information on this though. Either way, the way the brain interprets colors is extremely complicated, involving something known as the opponent process.
en.wikipedia.org/wiki/Opponent_process

Intro song: 1812 overture by Tchaikovsky (specifically the U Vorot Vorot part)
Outro song: Waltz of the Flowers also by Tchaikovsky

Chapters:
0:00 Intro
1:04 Cone cells
5:10 Spectral colors
8:20 Color spaces
13:34 Polychromatic light
16:13 Chromaticity diagram
21:09 Physics of reflection
23:25 Blackbody radiation
26:58 Luminescence
28:42 Computer Screens
30:58 Printers
32:28 RGB cube
35:23 HSV color space
40:00 Color schemes
41:46 outro

updated 2 years ago

The Amazing Math behind Colors!

Kuvina Saydaki 2022-08-12 | In this video, I talk about the math and science of colors for 42 minutes. Topics include cone cell response functions, electromagnetic radiation, spectral colors, luminance, color spaces, parametric equations, normal curves, mono and polychromatic light, emission spectra, spectral power distributions, chromaticity diagrams, linear transformations, the physics of diffuse reflection and light sources, blackbody radiation, sunlight, refraction, rainbows, rayleigh scattering, fluorescence, LEDs, color gamuts, CRT TV, LCD screens, CMYK printers, the RGB cube, binary, hexadecimal codes, the HSV color space, cylinder and cone, and color schemes. This is my entry in #SoME2

Corrections/Clarifications:
37:10 I misspoke and said m1 instead of m2. What is shown on screen is correct.
22:12 On screen it says λ = f/c, but this is wrong. The correct formula is λ = c/f
I have been told by some commenters that the long cone responsivity graph has a smaller, secondary peak, in the shorter wavelengths, and this is a reason why monochromatic violet appears more red than a pure blue. I have found conflicting information on this though. Either way, the way the brain interprets colors is extremely complicated, involving something known as the opponent process.
en.wikipedia.org/wiki/Opponent_process

Intro song: 1812 overture by Tchaikovsky (specifically the U Vorot Vorot part)
Outro song: Waltz of the Flowers also by Tchaikovsky

Chapters:
0:00 Intro
1:04 Cone cells
5:10 Spectral colors
8:20 Color spaces
13:34 Polychromatic light
16:13 Chromaticity diagram
21:09 Physics of reflection
23:25 Blackbody radiation
26:58 Luminescence
28:42 Computer Screens
30:58 Printers
32:28 RGB cube
35:23 HSV color space
40:00 Color schemes
41:46 outro

The ALMOST Perfect Numbers

Kuvina Saydaki 2024-08-06 | This is my entry in #SoMEpi . The perfect numbers are some of the most famous in all of number theory. But since perfection is so hard to achieve, we're naturally drawn to the mathematical quest for perfection. That manifests itself in the form of many types of almost perfect numbers.

70 is weird: youtube.com/watch?v=jrhVJKSKNwk

0:00 Intro
2:04 Descartes
6:06 Quasi perfect
8:11 Almost perfect
9:44 Aliquot sequences
15:37 Multiply perfect
19:00 Hemi perfect
20:06 Relative abundance clubs
22:51 Near perfect
24:43 Unitary perfect
26:46 Sublime
28:55 Outro

#math #numbertheory #perfectnumber

Visualizing 70 Sorting Algorithms

Kuvina Saydaki 2024-05-07 | Full explanation video: youtube.com/watch?v=h1Bi0granxM

This video shows off my sorting algorithm visualization program that I made with c++ and sfml. I programmed the algorithms myself in order to properly understand them for the explanation video. For smooth, poplar, wiki, and grail, I didn't have time to program them, so I used ArrayV. The sound effects in this video are mostly musescore samples or audacity generated tones, chirps, etc.

Chapters:
0:00 Selection
0:25 Double Selection
0:37 Insertion
1:00 Binary Insertion
1:14 Bubble
1:38 Shaker
2:01 Comb
2:21 Heap
2:43 Min Heap
2:55 Shell
3:24 Quick
3:47 Merge
4:15 Radix LSD (b = 4)
4:35 Radix LSD (b = 10)
4:52 Radix MSD (b = 4)
5:15 Radix MSD (b = 10)
5:33 Bucket (b = 10)
6:04 Bucket (b = n/10)
6:18 Counting
6:32 Gravity
6:45 Bogo
7:08 Pancake
7:37 Cycle
8:04 Exchange v1
8:28 Exchange v2
8:44 Odd Even
9:08 Gnome
9:32 Baiai
9:55 Circle
10:12 Patience (cheat version)
10:42 Strand (cheat version)
11:19 Bitonic
11:58 Recursive Bitonic
12:14 Alternate Bitonic
12:30 Bitonic w/ Parallel Processors
12:41 Odd Even Network
13:16 Pairwise Network
13:50 Quick LL
14:26 Dual Pivot Quick
14:59 Proportion Extend
15:28 Intro
16:00 Pattern Defeating Quick
16:29 Tim
17:07 Iterative Merge v1
17:31 Iterative Merge v2
17:56 In Place Merge (basic edition)
18:21 Weave
18:53 Rotate Merge
19:29 Quad
20:00 Weak Heap
20:38 Ternary Heap
21:21 Smooth
21:46 Poplar
22:01 In Place Radix MSD (b = 4)
22:30 Binary Quick (b = 2)
22:58 In Place Radix LSD (b = 4)
23:24 American Flag (b = 128)
23:40 Spread (b = n/10)
23:57 Sample (b = n/10, s = 2)
24:23 Proxmap (b = n/10)
24:43 Sqrt (Kuvi version)
25:20 Original Block
26:03 Wiki
26:33 Grail
27:11 Stooge
27:38 Slow
28:05 Stalin
28:15 Miracle
28:34 Identity Crisis
29:01 Quantum Bogo

#sorting #algorithms #computerscience #visualization #satisfying

Every Sorting Algorithm Explained in 120 minutes (full series)

Kuvina Saydaki 2024-05-07 | This is a compilation video of the 4 existing sorting videos on my channel.

Visualizations: youtu.be/Uq6URzo9q6g

youtube.com/watch?v=AAwYzYkjNTg
youtube.com/watch?v=wqibJMG42Ik
youtube.com/watch?v=FntVy6lPVyo
youtube.com/watch?v=InGeRuRk3f8

Corrections / clarifications: none so far

Resources I mentioned in section 4:
http://itbe.hanyang.ac.kr/ak/papers/tamc2008.pdf
en.wikipedia.org/wiki/Block_sort
github.com/BonzaiThePenguin/WikiSort
github.com/HolyGrailSortProject/Rewritten-Grailsort
https://habr-com.translate.goog/en/articles/205290/?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US&_x_tr_hist=true

Chapters:
0:00 Intro
1:34 Selection
2:04 Double Selection
2:30 Insertion
3:07 Binary Insertion
3:56 Bubble
4:28 Shaker
4:46 Asymptotic Notation
7:40 Finding Time Complexity
9:48 Quick
11:51 Merge
13:10 Stability
14:11 Space Complexity
15:57 Heap
18:46 Comb
20:05 Shell
21:28 Radix LSD
25:28 Radix MSD
26:11 Bucket
28:58 Counting
30:26 Spaghetti
31:03 Gravity
32:33 Pancake
33:45 Bogo
34:53 Section 2 Intro
35:16 Cycle
35:55 Patience
37:04 Exchange
37:49 Odd-Even
38:12 Circle
39:13 Merge-Insertion
40:13 Tournament
41:00 Tree
42:09 Gnome
42:41 Library
43:28 Strand
44:20 Topological Sorting
45:18 Sorting Networks
46:57 Bitonic
48:43 Odd-Even Network
49:07 Pairwise Network
49:42 Why Hybrid Algorithms?
52:34 Quick LL
52:59 Dual Pivot Quick
53:53 Proportion Extend
54:40 Intro
55:21 Pattern Defeating Quick
57:06 Tim
58:54 Iterative Merge
1:00:20 In Place Merge
1:01:10 Weave
1:01:42 Rotate Merge
1:02:59 Quad
1:04:37 Block Sort Preview
1:05:08 Weak Heap
1:08:19 Smooth
1:11:23 Poplar
1:11:52 Ternary Heap
1:12:26 In Place Radix MSD
1:13:45 Binary Quick
1:14:09 In Place Radix LSD
1:14:53 American Flag
1:15:57 Burst
1:16:21 Spread
1:17:19 Sample
1:18:05 Proxmap
1:18:24 Cartesian Tree
1:18:56 Section 4 Intro
1:23:05 Outline
1:25:29 Sqrt
1:30:05 Block
1:36:39 Wiki
1:41:57 Grail
1:50:07 Stooge
1:51:06 Slow
1:52:08 Quantum Bogo
1:52:33 Stalin
1:53:36 Sleep
1:53:56 Miracle
1:54:20 Bogobogo
1:55:24 Power
1:56:09 Outro

#math #sorting #algorithms #explained #math #computerscience

70 is a weird number #math #numbers #weird

Kuvina Saydaki 2024-04-13 | watch the full video on my channel!

70 is weird

Kuvina Saydaki 2024-04-08 | In math and number theory there are many sequences of numbers and one of the most interesting ones is the weird numbers! In this video, we examine the motivation behind them, especially abundant numbers, deficient numbers, perfect numbers, highly composite numbers, and practical numbers.

#math #70 #numbers

When velocities dont add (Relativity)

Kuvina Saydaki 2024-03-03 | Relativity is the idea that time and space behave differently depending on your perspective. One interesting consequence is that velocities do not add. They combine according to a specific formula, which is extremely fascinating, and the subject of this video.

Chapters:
0:00 Intro
1:27 When velocities do add
4:52 Derivation
8:53 Nice features of the formula
12:01 Tachyons
14:41 Outro

#math #science #physics #relativity

Mathematical Coincidences

Kuvina Saydaki 2024-02-01 | In this video we take a look at some fun mathematical coincidences!
#math
#weird
#coincidence
#funfacts

The Perfect Sorting Algorithm?? Block Sort Explained (Wiki Sort, Grail Sort)

Kuvina Saydaki 2023-11-22 | In this video, I explain the sorting algorithms sqrt sort, block sort, wiki sort, and grail sort. I used arrayV for the visuals for wiki sort and grail sort. If you want to learn more about them, then here are some resources:

Sqrt sort:
My version is basically the original block sort without the buffers, but the version on arrayV seems to be grail sort without the buffers.

Original blocks sort:
It comes from this 2008 paper
http://itbe.hanyang.ac.kr/ak/papers/tamc2008.pdf

Wiki sort:
The wikipedia of block sort describes wiki sort, but only ever calls it block sort
en.wikipedia.org/wiki/Block_sort
And here's the github project of wiki sort
github.com/BonzaiThePenguin/WikiSort

Grail sort:
Here's the github project of grail sort rewritten, which is part of the larger holy grail sort project
github.com/HolyGrailSortProject/Rewritten-Grailsort
And I figured out grail sort from this google translated article (the original is in Russian)
https://habr-com.translate.goog/en/articles/205290/?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US&_x_tr_hist=true

Chapters:
0:00 Intro
4:48 Outline
7:20 Sqrt sort
11:52 Original block sort
18:18 Wiki sort
23:44 Grail sort
30:47 Outro

#math #computerScience #sorting #algorithm

The Ladder Paradox Explained

Kuvina Saydaki 2023-09-26 | Relativity is the idea that time and space can behave differently depending on your perspective. It is notoriously difficult to understand, but in this series, I explain the methods that helped me understand it to the best of my ability.

playlist: youtube.com/watch?v=qBsw3rXgJZs&list=PLOMmeEsL7dq-fVnQGQwVJeKZxvl0kdjIp

#relativity #science #physics

Explaining EVERY Sorting Algorithm: Variants and Hybrids

Kuvina Saydaki 2023-09-14 | This is the 3rd episode in my series explaining every sorting algorithm. In this video, I explain the most widespread hybrid and variant sorting algorithms.
part 1: youtu.be/AAwYzYkjNTg
part 2: youtu.be/wqibJMG42Ik

twitter: twitter.com/kuvina_4
instagram: instagram.com/kuvina_4

Chapters:
0:00 Why Hybrid Algorithms?
2:36 Quick Sort with LL Pointers
3:01 Dual Pivot Quick Sort
3:55 Proportion Extend Sort
4:42 Intro Sort
5:23 Pattern-Defeating Quick Sort
7:08 Tim Sort
8:56 Iterative Merge Sort
10:00 In Place Merge Sort
11:12 Weave Sort
11:30 Rotate Merge Sort
13:01 Quad Sort
14:40 Block Sort
16:18 Weak Heap Sort
19:09 Smooth Sort
22:35 Poplar Sort
23:05 Ternary Heap Sort
23:39 In Place MSD Radix Sort
24:57 Binary Quick Sort
25:21 In Place LSD Radix Sort
26:05 American Flag Sort
27:10 Burst Sort
27:34 Spread Sort
28:31 Sample Sort
29:18 Proxmap Sort
29:37 Cartesian Tree Sort
30:09 Stalin Sort
31:16 Sleep Sort
31:36 Miracle Sort
32:00 Bogobogo Sort
33:04 Power Sort
33:50 Identity Crisis Sort
34:20 Outro Sort

#sorting #algorithm #computerscience

The ALMOST Platonic Solids

Kuvina Saydaki 2023-08-11 | This is my entry in #SoME3 . This video covers the Archimedean solids, Catalan solids, and Johnson solids. Geometry is one of the most beautiful parts of math, and polyhedra are one of my favorite parts of that. If you love geometry, make sure to check out my video on map projections!

Chapters:
0:00 Intro
1:17 Archimedean Solids
7:22 Proving there are 13
12:13 Catalan Solids
18:28 Johnson Solids
27:11 Outro

#math #geometry

Every Sorting Algorithm (part 2): The Weird and Obscure

Kuvina Saydaki 2023-07-09 | ATTENTION: This is part 2 of my series on sorting algorithms, but I recently changed the title and thumbnail slightly.

In this episode, I explain some weird and obscure sorting algorithms.
part 1: youtu.be/AAwYzYkjNTg
twitter: twitter.com/Kuvina_4

Chapters:
0:00 Intro
0:35 Cycle
1:14 Patience
2:23 Exchange
3:08 Odd-Even
3:42 Circle
4:43 Merge-Insertion
5:43 Tournament
6:29 Tree
7:39 Gnome
8:11 Library
8:59 Strand
9:50 Topological
10:48 Sorting Networks
12:18 Bitonic
14:13 Odd Even Network
14:37 Pairwise Network
15:13 Stooge
16:03 Slow
17:04 Quantum Bogo
17:28 Thank you!

#sorting #algorithm #computerscience

Explaining EVERY Sorting Algorithm (part 1)

Kuvina Saydaki 2023-06-07 | There are lots of sorting algorithms and some of them are hard to understand, so in this series I will explain all of them, starting in part 1 with those that I consider most important to understand.

corrections/clarifications: none so far

Chapters:
0:00 Intro
1:04 Selection Sort
1:35 Double Selection Sort
2:01 Insertion Sort
2:38 Binary Insertion Sort
3:27 Bubble Sort
3:59 Shaker Sort
4:21 Asymptotic Notation
7:11 Finding Time Complexity
8:57 Quick Sort
11:22 Merge Sort
12:40 Stability
13:42 Space Complexity
15:28 Heap Sort
18:17 Comb Sort
19:35 Shell Sort
20:59 Radix Sort
24:59 MSD Radix Sort
25:42 Bucket Sort
28:34 Counting Sort
29:52 Spaghetti Sort
30:34 Gravity Sort
32:00 Pancake Sort
33:15 Bogo Sort
34:25 Outro

Length Contraction Explained

Kuvina Saydaki 2023-03-06 | Relativity is the idea that time and space can behave differently depending on your perspective. It is notoriously difficult to understand, but in this series, I explain the methods that helped me understand it to the best of my ability. This episode covers length contraction, where the lengths of objects change depending on velocity.

Intro Song: Chopin's Nocturne op 9 no 2, performed by Frank Levy
commons.wikimedia.org/wiki/File:Nocturne_in_E_flat_major,_Op._9_no._2.mp3
Outro Song: Tchaikovsky's Waltz of the Flowers, from youtube's media library

Relativity of Simultaneity

Kuvina Saydaki 2022-06-24 | Relativity is the idea that time and space can behave differently depending on your perspective. It is notoriously difficult to understand, but in this series, I explain the methods that helped me understand it to the best of my ability. This episode is about relativity of simultaneity, where 2 events can be simultaneous in one reference frame, but not in another.

Also, no this is not my some2 entry. That will hopefully be the next video.

Intro song: 1812 overture by Tchaikovsky (specifically the U Vorot Vorot part)
Outro song: Waltz of the Flowers also by Tchaikovsky

How I made my own Fractal

Kuvina Saydaki 2022-05-31 | In this video I explain how I came up with my own fractal and also how you can do the same.

Music used: 1812 overture and waltz of the flowers both by Tchaikovsky

chapters:
0:00 intro
0:46 how it works
2:29 Level 4
3:43 other levels
8:20 shadow versions
9:12 bi versions
10:58 shadow skew
12:02 psychedelic versions
13:04 shadow psych
13:43 product versions
16:27 outro

Time Dilation Explained

Kuvina Saydaki 2022-05-18 | Relativity is the idea that time and space can behave differently depending on your perspective. It is notoriously difficult to understand, but in this series, I explain the methods that helped me understand it to the best of my ability. This episode is about time dilation, in which time passes at different rates depending on your reference frame.

Clarification: The international space station is technically not an inertial reference frame. It's orbiting, which is a form of acceleration. This doesn't make much of a difference, so I used it as an example, because it's a very tangible way of understanding. It's worth noting though, that the time dilation on the ISS is partially caused by its velocity, but is also partially caused by the earth's gravitational effects. Gravitational time dilation is part of general relativity though, so I deliberately chose not to mention it for the sake of the example.

Intro song: 1812 overture by Tchaikovsky (specifically the U Vorot Vorot part)
Outro song: Waltz of the Flowers also by Tchaikovsky

Relativity Explained: Reference Frames and Postulates

Kuvina Saydaki 2022-03-13 | Relativity is the idea that time and space can behave differently depending on your perspective. It is notoriously difficult to understand, but in this series, I explain the methods that helped me understand it to the best of my ability.

clarification: In the video, I said that acceleration is not relative, and therefore absolute. Is acceleration absolute? Not necessarily, it's just that relativity subtly postulates that it is. It's perfectly reasonable to treat acceleration as absolute in the context of relativity, but if you want to learn more about the absoluteness of acceleration, you should definitely look into the bucket argument. It's actually quite a controversial subject in the philosophy of physics.
en.wikipedia.org/wiki/Bucket_argument
en.wikipedia.org/wiki/Philosophy_of_space_and_time

Map Projections Explained

Kuvina Saydaki 2021-08-18 | Correction: The azimuthal equidistant projection is actually defined by θ = a and r = 90° - b. I got b mixed up with phi.

This video was made for 3blue1brown's summer of math exposition contest. It was selected as one of the top 100, and that has really helped kickstart my channel, so a huge thank you goes out to 3blue1brown.

Note: If the title changes, it's because I'm testing out different video titles to see what works the best.

In this video, I explain map projections: what they are, how they work, and the math behind them. This video connects 2 of my favorite subjects: math and geography. If you want to do further research, this wikipedia page is very helpful:
en.wikipedia.org/wiki/List_of_map_projections

The images of each projection come from that page, and are made by Daniel R. Strebe.

Chapters:
0:00 Intro
0:41 The Problem
3:37 Equirectangular Projection
7:15 Literal Projection
9:49 Mercator Projection
18:51 Sinusoidal Projection
21:24 Lambert Equal Area Projection
23:33 Azimuthal Equidistant Projection
24:30 Compromises
29:30 Perspectives
31:21 Conclusion

How many countries are there???

Kuvina Saydaki 2021-07-20 | Corrections or clarifications: None so far. Please tell me if you find a mistake.

Welcome to my first video! In this video, I answer how many countries there are to the best of my ability. I expect that this video will get very few views if any, so I really appreciate if you like and subscribe. Most importantly though, comment! You can tell me what you thought of the video, how to improve my style, ideas for the future, or anything really (just make sure to be respectful).

Chapters:
00:00 Intro
01:15 UN countries
03:07 Unrecognized Countries
09:41 Constituent Countries
10:32 Associated Territories
11:19 Dependent Territories
13:57 Interpretations
16:16 Stretches
18:18 The Future
19:25 Conclusion

If you want to research the subject on your own, then here are some links that I think are very helpful:
en.wikipedia.org/wiki/List_of_states_with_limited_recognition
en.wikipedia.org/wiki/Dependent_territory
simple.wikipedia.org/wiki/Constituent_country
en.wikipedia.org/wiki/Quasi-state