The Surprising Maths of Britains Oldest* Game Show Another Roof 2023-01-26 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬣ ABOUT ⬣First broadcast in 1982, Countdown is iconic British TV. Its numbers game is the perfect balance of challenge and simplicity. In this video, I analyse the hidden mathematics of the game: What are the hardest targets, best numbers to draw, and optimal tactics?⬣ TIMESTAMPS ⬣00:00 - Introduction04:46 - How Many Possible Games?10:00 - Reachable Numbers from a Given Game Set14:00 - Results and Tactics: Small Numbers24:00 - Results and Tactics: Large Numbers31:00 - Scary Numbers40:05 - Outro⬣ CHALLENGE ⬣So to clarify, I want to see a list of the percentage of solvable games for ALL options of large numbers. Like I did for the 15 options of the form {n, n+25, n+50, n+75}, but for all of them. The options for large numbers should be four distinct numbers in the range from 11 to 100. As I said there are 2,555,190 such options so this will require a clever bit of code, but I think it’s possible! Email me via my website if you think you have it!⬣ FILES ⬣drive.google.com/drive/folders/1tEPJU55mxIlTLO2fzvtVhdTgnIhv3FKp?usp=sharing⬣ INVESTIGATORS ⬣I’ve never seen that colour on my screen before. I’m hoping you excel yourself and slug out the solution. Now is the perfect time to join the investigation.⬣ REFERENCES ⬣wiki.apterous.org/CECILBlog I mention which uses reverse Polish notation:datagenetics.com/blog/august32014/index.html⬣ CREDITS ⬣All music by Danjel Zambo.ImagesRachel Riley: commons.wikimedia.org/wiki/File:Rachel_Riley_2011.JPGCarol Vorderman: upload.wikimedia.org/wikipedia/commons/b/b2/Carol_Vorderman_Waddington_Airshow_2011_-3.jpgTeapot: upload.wikimedia.org/wikipedia/commons/3/3b/Teapot.jpgCecil Korer: wiki.apterous.org/images/c/c5/Cecil_Korer.JPGOK Emoji: upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Emoji_u1f44c.svg/640px-Emoji_u1f44c.svg.pngB Footage8 Out of 10 Cats Does Countdown, Countdown © Channel 4.The Chase © ITV.Have I Got News for You, Only Connect, Pointless, Richard Osman’s House of Games, University Challenge, The Weakest Link, Would I Lie to You? © BBC.Des Chiffres et Des Lettres © France 3.
Why Navy Enigma was Different w/ James Grime Another Roof 2024-10-01 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣I had no idea that the systems surrounding the Navy Enigma machine were completely different to that of the Army, making the code much tougher to crack. In this video, James teaches me these differences and discusses what Alan Turing managed to achieve in breaking this code.⬣ TIMESTAMPS ⬣⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ CREDITS ⬣Music by Danijel Zambo, Tobias Voigt, and Apex Music.Numberphile: Enigma Videoyoutube.com/watch?v=G2_Q9FoD-oQIMAGESEnigma Monthly Settings Documentciphermachinesandcryptology.com/en/enigmaproc.htmEnigma Bigram Tableciphermachinesandcryptology.com/img/enigma/bigram-fluss-b.jpgEnigma Triplets Documentciphermachinesandcryptology.com/img/enigma/kenngruppenbuch4.jpg
A Poor Imitation: The Real Alan Turing w/ James Grime Another Roof 2024-08-16 | FlexiSpot 8th Anniversary!Get the chance to get the E7 PRO at 50% off on August 19Anniversary Sale - bit.ly/3LrzWLbGet my premium E7 PRO desk here- bit.ly/4cBWntg#flexispotuk⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣Alan Turing: WW2 hero, father of computing, and played by Benedict Cumberbatch in 2014 biopic "The Imitation Game". James Grime joins me to analyse this film and how some of its historical inaccuracies were a disservice to Turing's character.⬣ TIMESTAMPS ⬣00:00 - Intro01:30 - The Imitation Game -- Accuracy11:10 - A Disservice to Turing16:37 - Turing, Computers, and AI24:52 - Verdict⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ CREDITS ⬣Music by Danijel Zambo, Tobias Voigt, and Apex Music.The Imitation Game footage (C) The Weinstein CompanyArticle on Alastair Dennistonnews.sky.com/story/alastair-denniston-familys-book-of-codebreaking-chief-to-counter-hollywood-portrayal-11019664Information is Beautiful Articleinformationisbeautiful.net/visualizations/based-on-a-true-true-storyNumberphile: Enigma Videoyoutube.com/watch?v=G2_Q9FoD-oQMinutePhysics: What is Fireyoutube.com/watch?v=1pfqIcSydgEVeritasium: How Does Earth Spin?youtube.com/watch?v=9zso7ChaQXQIMAGESBombeupload.wikimedia.org/wikipedia/commons/7/7a/Wartime_picture_of_a_Bletchley_Park_Bombe.jpgAlan Turing Buildingupload.wikimedia.org/wikipedia/commons/3/39/Alan_Turing_Building_2.jpgDaniel Radcliffemetro.co.uk/wp-content/uploads/2023/06/GettyImages-1384684390.jpg?quality=90&strip=allAlan Turingbritannica.com/biography/Alan-TuringTuring Letterhttps://i.guim.co.uk/img/static/sys-images/Guardian/Pix/pictures/2015/8/22/1440246760260/48bf3bfa-c14f-48b4-b882-6f5248ae2522-542x720.jpeg?width=1140&dpr=1&s=none
Thats Not How the Golden Ratio Works Another Roof 2024-07-28 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣There’s much to admire about the Golden Ratio, but its significance is largely overblown. In this video, we separate some of the facts from the fiction, while analysing Darren Aronofsky’s “Pi”.⬣ TIMESTAMPS ⬣00:00 - Intro02:57 - What is the Golden Ratio?04:53 - The Fibonacci Sequence and the Golden Ratio10:54 - Nature and Diophantine Approximation15:14 - Hurwitz’s Inequality21:20 - Numerology and Gematria26:09 - Is Pi Good?29:02 - Verdict⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ SEE ALSO ⬣Numberphile video featuring Ben Sparks:youtube.com/watch?v=sj8Sg8qnjOgAstrology Future Eyeastrologyfutureeye.com/numerology/pythagorean-numerologyAssassinations Foretold in Moby Dick! by Brendan McKayhttps://users.cecs.anu.edu.au/~bdm/dilugim/moby.html⬣ REFERENCES ⬣G. H. Hardy, E. M. Wright: “An Introduction to the Theory of Numbers” Fourth Edition. Oxford University Press (1960).⬣ CREDITS ⬣Music by Danijel Zambo, Tobias Voigt, and Apex Music.Pi (film) footage (C) Protozoa Pictures, Artisan Entertainment, Summit Entertainment.Requiem for a Dream footage (C) Thousand Words, Protozoa Pictures, Artisan Entertainment, Summit Entertainment.IMAGESGearships.hearstapps.com/popularmechanics/assets/16/23/1465575513-gears.jpgMonty Hallen.wikipedia.org/wiki/Monty_Hall_problem#/media/File:Monty_open_door.svgGolden Spiralelegantthemes.com/blog/wp-content/uploads/2019/06/Ratio-768x486.pngSacred Creationsacredgeometryshop.com/sacred-geometry/sacred-geometry-numerologyJeevesreddit.com/media?url=https%3A%2F%2Fpreview.redd.it%2Fu0v7ecfl8lm51.jpg%3Fauto%3Dwebp%26s%3D8e0cb5aba8041ae18479fb74bf4aef2b12b40b1d8 Mile poster (C) Universal PicturesMona Lisaen.wikipedia.org/wiki/Mona_Lisa#/media/File:Mona_Lisa,_by_Leonardo_da_Vinci,_from_C2RMF_retouched.jpgParthenoncdn.hswstatic.com/gif/parthenon-golden-ratio-orig.jpgArchimedean Spiralen.wikipedia.org/wiki/Archimedean_spiral#/media/File:Archimedean_spiral.svgEuler Spiralen.wikipedia.org/wiki/Euler_spiral#/media/File:Euler_spiral.svgSpiral: From the Book of Saw (C) Universal PicturesLogarithmic Spiralen.wikipedia.org/wiki/Logarithmic_spiral#/media/File:Logarithmic_Spiral_Pylab.svgSunflowersynchronicitypc.com/wp-content/uploads/2019/08/SunflowerTheScienceExplorer.jpgParthenon with Golden Rectanglecdn.shopify.com/s/files/1/0608/0643/0949/files/3_480x480.png?v=1642310689Pineconehttps://i.pinimg.com/originals/f8/87/52/f88752dc9998062e03266b8631c2ee35.jpgPineappleencrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSuYQN7eNsFkSWnHWimrA6XhaXl1kNEe8xQmA&sAdolf Hurwitzupload.wikimedia.org/wikipedia/commons/d/d1/Adolf_Hurwitz.jpgNautilus Shelllive.staticflickr.com/7233/7351300052_b5135abb54_b.jpgMilky Waycdn.mos.cms.futurecdn.net/D7AzRK9mDsZnBecvdMhr5Y.jpgHurricane Katrinaupload.wikimedia.org/wikipedia/commons/thumb/a/af/Katrina_2005-08-28_1700Z.jpg/800px-Katrina_2005-08-28_1700Z.jpg
Why are Most Polygons Impossible to Construct? Another Roof 2024-06-05 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣Only certain regular polygons are constructible with compass and straightedge. Why? And why did the first person to prove it after 2000 years get no recognition? In this introduction to Field Theory, we’ll find out, and along the way we’ll also prove other impossibilities like why cube doubling and angle trisection are impossible. Happy Birthday Pierre Wantzel!⬣ TIMESTAMPS ⬣00:00 - Intro02:13 - Why ONLY the four operations and Square Roots04:14 - Field Extensions14:37 - Minimal Polynomials25:54 - Cube Doubling is Impossible31:50 - Angle Trisection is Impossible36:35 - Constructible Polygons: The Gauss-Wantzel Theorem50:12 - Why Pierre Wanzel got No Recognition⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ REFERENCES ⬣Biographical details on Wantzel to be found in:Jean-Claude Saint-Venant (1848). “Biographie: Wantzel”. Nouvelles Annales de Mathématiques Série 1, 7: 321-331.Found, with English translation by Lauren Murphy, here: divisbyzero.com/wp-content/uploads/2018/02/saint-venant.pdfAmazing treatise on possible reasons why Wantzel was never credited:Jesper Lützen, “Why was Wantzel Overlooked for a Century? The Changing Importance of an Impossibility Result” Historia Mathematica, Vol 36 (4) 374-394, 2009.Found here: sciencedirect.com/science/article/pii/S031508600900010XPierre Wantzel’s original paper, with proofs adapted in the video:Wantzel, L. (1837), "Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas", Journal de Mathématiques Pures et Appliquées, 2: 366–372.Found here: http://visualiseur.bnf.fr/ConsulterElementNum?O=NUMM-16381&Deb=374&Fin=380&E=PDF⬣ CREDITS ⬣Music by Danijel Zambo, Tobias Voigt, and Apex Music.Image CreditsWantzelmathshistory.st-andrews.ac.uk/Biographies/Wantzel/poster/livedHamiltonupload.wikimedia.org/wikipedia/commons/f/f6/William_Rowan_Hamilton_portrait_oval_combined.pngKleinupload.wikimedia.org/wikipedia/commons/4/4e/Felix_Klein%2C_ante_1897_-_Accademia_delle_Scienze_di_Torino_0078_B.jpgDe Morganupload.wikimedia.org/wikipedia/commons/2/2c/De_Morgan_Augustus.jpgPetersenupload.wikimedia.org/wikipedia/commons/6/65/Petersen_Julius.jpgPascal's Trianglegeogebra.org/resource/jk42jcvy/wp6YMh81jzMYSh2D/material-jk42jcvy.png
It Took 2137 Years to Solve This Another Roof 2024-04-30 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣Despite being easy to state, the problem of constructing regular polygons confounded the Ancient Greeks. It took over 2000 years to make progress, and in this video we’ll trace a path through history to learn what innovations allowed more polygons to be constructed.⬣ TIMESTAMPS ⬣00:00 - Introduction01:47 - Ancient Constructions08:14 - What the Ancient Greeks Lacked11:20 - From Geometry to Numbers16:28 - From Numbers to Equations21:58 - From Equations to the Complex Plane31:48 - Gaussian Periods36:10 - Final Construction⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ REFERENCES ⬣Euclid's constructions mentioned at 3:50:Perpendicular lines: http://aleph0.clarku.edu/~djoyce/elements/bookI/propI11.htmlDuplicate angles: http://aleph0.clarku.edu/~djoyce/elements/bookI/propI23.htmlAlternate angles: http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI29.htmlParallel lines: http://aleph0.clarku.edu/~djoyce/elements/bookI/propI31.htmlParallelogram properties: http://aleph0.clarku.edu/~djoyce/elements/bookI/propI34.htmlThe Thirteen Books of Euclid’s Elements. T. L. Heath (1908)J. Derbyshire: "Unknown Quantity: A Real and Imaginary History of Algebra" Joseph Henry Press (2006)Al-Kamil treats irrational quantities as numbers in their own rightH. Selin, U. D'Ambrosio: "Mathematics Across Cultures: The History of Non-Western Mathematics" Springer (2000)Al-Mahani’s definition of rational and irrationalM. Galina: "The theory of quadratic irrationals in medieval Oriental mathematics" Annals of the New York Academy of Sciences 500 (1987) 253-277.Al-Khwaizmi quadratic equationsAl-Jabr - Al KhwarizmiSridhara’s methodD. E. Smith: “History of Mathematics” Vol 2 Dover (1925)Tombstone storyC. W. Dunnington: "Carl Friedrich Gauss: Titan of Science" Hafner Publishing (1955)⬣ CREDITS ⬣Intro music by Tobias Voigt. Other music by Danijel Zambo and Apex Music.Image CreditsEuclidcdn.britannica.com/46/8446-050-BC92B998/Euclid-woodcut-1584.jpgArithmeticaupload.wikimedia.org/wikipedia/commons/3/3b/Diophantus-cover.pngAl-Jabrupload.wikimedia.org/wikipedia/commons/2/25/Bodleian_MS._Huntington_214_roll332_frame36.jpgGaussupload.wikimedia.org/wikipedia/commons/e/ec/Carl_Friedrich_Gauss_1840_by_Jensen.jpgHeptadecagon Constructionupload.wikimedia.org/wikipedia/commons/d/d1/Regular_Heptadecagon_Inscribed_in_a_Circle.gifGauss Tombstoneupload.wikimedia.org/wikipedia/commons/2/26/Grave_of_Carl_Friedrich_Gau%C3%9F_at_Albani-Friedhof_G%C3%B6ttingen_2017_02.jpg
AI Can Do Maths Now, and its Wild Another Roof 2024-03-17 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroofCheck out Sabine Hossenfelder’s video here:youtube.com/watch?v=NrNjvIrCqII⬣ ABOUT ⬣AlphaGeometry is a new AI system developed by DeepMind that can solve Olympiad-level geometry problems. This has been hailed as a leap forward in AI reasoning, but is it? In this video, break down how AlphaGeometry works and give my general thoughts on the use of AI in mathematics.⬣ TIMESTAMPS ⬣00:00 - Introduction01:04 - How Does AlphaGeometry Work?02:27 - Triangle Facts03:55 - IMO 2008: Problem 1 (Setup)06:50 - IMO 2008: Problem 1 (AlphaGeometry’s Solution)13:11 - IMO 2008: Problem 1 (Discussion)18:22 - Is AlphaGeometry Good at Mathematics?22:21 - The Use of AI in Mathematics: Good or Bad?⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ REFERENCES ⬣Trinh, T.H., Wu, Y., Le, Q.V. *et al. “*Solving olympiad geometry without human demonstrations.” *Nature* **625**, 476–482 (2024). doi.org/10.1038/s41586-023-06747-5K. Appel and W. Haken “The Existence of Unavoidable Sets of Geographically Good Configurations” Illinois J. Math. 20 (1976), 218-297⬣ CREDITS ⬣MusicIntro music by Tobias Voigt. Other music by Danjel Zambo and Apex Music.ImagesDeep Blue vs Garry Kasparov (C) Adam Nadel, AP Imagesbritannica.com/topic/Deep-BlueWatson on Jeopardyhttps://i.ytimg.com/vi/P18EdAKuC1U/maxresdefault.jpgAlphaGo vs Lee Sedolstorage.googleapis.com/gweb-uniblog-publish-prod/images/AlphaGo_hero.width-1200.format-webp.webpElementschristies.com/en/lot/lot-6382657Kasparov Newspapersecure-images.rarenewspapers.com/ebayimgs/6.g3.2022/image002.jpgWileshttps://i.guim.co.uk/img/media/f809427647f499fcc6b26def9cc64b897abe01f1/1_4_1790_1074/master/1790.jpg?width=1200&quality=85&auto=format&fit=max&s=00cfd24886f1be0d486658d66eb64a1bFour Colour TheoremTaken from K. Appel and W. Haken “The Existence of Unavoidable Sets of Geographically Good Configurations” Illinois J. Math. 20 (1976), 218-297Fluid Simulationyoutube.com/watch?v=03Hq_OTa-gA
The Ancient Mathematics of the DVD Screensaver Another Roof 2024-01-31 | To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/AnotherRoofThe first 200 of you will get 20% off Brilliant’s annual premium subscription.⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣We've all seen the beloved DVD Screensaver and been excited to see it hit the corner. But is this guaranteed to happen? If it happens once, will it happen again? And long will you have to wait between corner hits? All these questions answered and more via the ancient number theory of Euclid and Diophantine. Spreadsheet here:drive.google.com/file/d/1xccmF7gBFVjcdsquxhs3enGnz8eSq6mQ/view?usp=sharingComputerCow video on the topic:youtube.com/watch?v=saq3JGOsB3M⬣ TIMESTAMPS ⬣00:00 - Introduction03:03 - Simplifying the Problem 108:40 - Simplifying the Problem 214:14 - Diophantine Equations21:44 - Euclidean Algorithm31:15 - Solution36:21 - Extra Questions⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ CREDITS ⬣Music by Danjel Zambo."Bionic" by Tobias Voigt."Cautious Optimism" by Apex Music.IMAGE CREDITSSmartwatchtrustedreviews.com/wp-content/uploads/sites/54/2022/08/Galaxy-Watch-5-Pro-apps-920x693.jpgDashboardcarscoops.com/wp-content/uploads/2020/10/2021-Cadillac-Escalade-42-1024x555.jpgiPhone 13trustedreviews.com/wp-content/uploads/sites/54/2021/09/iphone-13-8-920x613.jpegSquare Latticeupload.wikimedia.org/wikipedia/commons/thumb/6/63/SquareLattice.svg/2560px-SquareLattice.svg.pngEquilateral Triangle Latticeupload.wikimedia.org/wikipedia/commons/thumb/9/97/Equilateral_Triangle_Lattice.svg/2048px-Equilateral_Triangle_Lattice.svg.pngRhombic Latticeupload.wikimedia.org/wikipedia/commons/thumb/2/28/Rhombic_Lattice.svg/2560px-Rhombic_Lattice.svg.pngAndrew Wilesupload.wikimedia.org/wikipedia/commons/4/4c/Andrew_wiles1-3.jpgFermatupload.wikimedia.org/wikipedia/commons/f/f3/Pierre_de_Fermat.jpgArithmeticaupload.wikimedia.org/wikipedia/commons/3/3b/Diophantus-cover.pngEtienne Bezoutupload.wikimedia.org/wikipedia/commons/9/92/Etienne_Bezout2.jpgB-ROLL CREDITS"How LED and LCD TV's Work in Slow Motion [Original]" - Warped Perceptionyoutube.com/watch?v=131S82R5Jjg"Happiness comes from the simple things" - SpartaYoshiyoutube.com/watch?v=m8NAlDOCG6g"Bouncing DVD Logo Screensaver 4K 60fps - 10 hours NO LOOP" - Raúl Blancoyoutube.com/watch?v=5mGuCdlCcNMThis video was sponsored by Brilliant.
The Film with the Most Maths Another Roof 2023-12-28 | To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/AnotherRoofThe first 200 of you will get 20% off Brilliant’s annual premium subscription.⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣X+Y (known in the US as "A Brilliant Young Mind") follows Nathan, an autistic teen who pursues his dream of competing in the International Mathematical Olympiad. This film has a surprising number of fully-stated problems that I break down in this video.Check out Mathologer's video on the cards problem here: youtu.be/04x4ZdLpN-0?si=XrMdD4KJVZyhpaX2⬣ TIMESTAMPS ⬣00:00 - Intro02:54 - Problem 109:15 - Problem 213:54 - Problem 315:02 - Problem 419:16 - Autism in X+Y22:30 - Discussion of the Film28:36 - Verdict⬣ CREDITS ⬣Music by Danjel Zambo and Tobias Voigt."Leaving" by Cory Alstad.Image CreditsCatalan's Identity, Wolfram Mathworldmathworld.wolfram.com/CatalansIdentity.htmlMiggy Billersome.ox.ac.uk/wp-content/uploads/2016/01/MiggyWEB.jpgHugo © Paramount Picturesresizing.flixster.com/-XZAfHZM39UwaGJIFWKAE8fS0ak=/v3/t/assets/p8403456_p_v10_aq.jpgEnder's Game © Lionsgateresizing.flixster.com/-XZAfHZM39UwaGJIFWKAE8fS0ak=/v3/t/assets/p9983313_p_v8_ac.jpgMartin Phippshttps://lokutusost.ufouni.cz/filmmusic/phipps/biography/Black Mirror: The National Anthem © Channel 4https://4.bp.blogspot.com/-dMnybe4ClNc/VKGu-a9z0lI/AAAAAAAALH4/F-Vlt5JfXE4/s1600/black1x1.jpgDaniel Lightwing - Photo by Matthew Lloydthetimes.co.uk/imageserver/image/%2Fmethode%2Ftimes%2Fprodmigration%2Fweb%2Fbin%2Fa1119f1c-5c3c-3116-a75b-7ea70fce77ee.jpg?crop=780%2C520%2C0%2C0&resize=1500B-Footage Credits - Adapted for this video under Fair UseX+Y footage © BBC Films and Plaion (formerly known as Koch Media)This video is sponsored by Brilliant.
How Hard is an Oxford Maths Interview? Feat. Tom Rocks Maths Another Roof 2023-11-26 | To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/AnotherRoofThe first 200 of you will get 20% off Brilliant’s annual premium subscription.Be sure to check out part 2 over on Tom's awesome channel!youtu.be/efXbABwhCtE?si=My_3wwraqOSyOK5B⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣After failing to score an interview with the University of Oxford back in the day, I've always wondered what the process is like. Luckily for me, Dr Tom Crawford is a fellow maths YouTuber who was all too happy to ask me some interview questions!This video was sponsored by Brilliant.
The Mathematical Storytelling of Cube Another Roof 2023-11-19 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣Cube is a 1997 horror film in which a group of strangers wake up in a 3D maze filled with traps. Escape relies on their ability to crack the mathematical puzzle of the cube's construction. But does the mathematics in the film stand up to scrutiny?⬣ TIMESTAMPS ⬣00:00 - Intro00:53 - Mathematics of the Rooms09:51 - Mathematics of the Traps11:59 - Quality16:05 - Verdict⬣ CREDITS ⬣Music by Danjel Zambo and Tobias Voigt.Image CreditsStephen Wiltshirecommons.wikimedia.org/wiki/File:Stephen_Wiltshire_IMG_3052_%2830608729825%29.jpgB-Footage Credits - Adapted for this video under Fair UseCube Footage © Cineplex Odeon Films, Trimark PicturesSaw © Lions Gate Films12 Angry Men © United ArtistsCircle © FilmBuff⬣ REFERENCES ⬣[1] - Treffert DA. The savant syndrome: an extraordinary condition. A synopsis: past, present, future. Philos Trans R Soc Lond B Biol Sci. 2009 May 27;364(1522):1351-7. doi: 10.1098/rstb.2008.0326. PMID: 19528017; PMCID: PMC2677584.
How π Emerges From a Forgotten Curve Another Roof 2023-10-31 | To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/AnotherRoof. The first 200 of you will get 20% off Brilliant’s annual premium subscription.⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣Happy Halloween! The Leibniz Formula -- the alternating sum of the reciprocals of odd numbers -- converges on π/4. It's a bizarre result. Even more bizarre is the Witch of Agnesi, a curve with a fascinating history. In this video we marry these together, using the Witch to demonstrate why this alternating sum produces π.This video was sponsored by Brilliant.⬣ TIMESTAMPS ⬣00:00 - Introduction03:37 - Defining the Witch07:49 - Two Lemmas11:56 - Witch Area Part I13:40 - Etymology of the Witch18:39 - Witch Area Part II28:55 - Outro⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ REFERENCES ⬣[1] P. Fermat, Œuvres de Fermat, Methodes de Quadrature, Gauthier-Villars et fils (1891). [2] G. Grandi, "Note al trattato del Galileo del moto naturale accellerato", Opera Di Galileo Galilei (in Italian), vol. III, Florence p. 393 (1728).[3] M. Agnesi, Instituzioni analitiche ad uso della gioventú (1748).[4] J. Colson, Analytical institutions, Wingrave & Rivington (1801).[5] smithsonianmag.com/science-nature/18th-century-lady-mathematician-who-changed-how-calculus-was-taught-180969078[6] D. Struik, A Source Book in Mathematics, Cambridge, Massachusetts: Harvard University Press (1969).[7] Complete Dictionary of Scientific Biography, Charles Scribner's Sons (Vol. 1.) (2008).[8] C. Truesdell, Corrections and additions for “Maria Gaetana Agnesi”. Arch. Hist. Exact Sci. 43, 385–386 (1992). doi.org/10.1007/BF00374764[9] P. Fanfani, Vocabolario dell'uso toscano, p. 334 (1863).[10] S. Stigler, Studies in the History of Probability and Statistics. XXXIII Cauchy and the witch of Agnesi: An historical note on the Cauchy distribution, Biometrika, Volume 61, Issue 2, August 1974, Pages 375–380, doi.org/10.1093/biomet/61.2.375[11] T. F. Mulcrone, The Names of the Curve of Agnesi. American Mathematical Monthly, 64, 359 (1957).[12] encyclopedia.com/women/encyclopedias-almanacs-transcripts-and-maps/agnesi-maria-gaetana-1718-1799⬣ IMAGE CREDITS ⬣Cauchy Distributionupload.wikimedia.org/wikipedia/commons/4/47/CauchyVerteilung.PNGSolitoncommons.wikimedia.org/wiki/File:Soliton_hydro.jpgWitchesen.wikipedia.org/wiki/Witch_of_Agnesi#/media/File:Witch_of_Agnesi_curves.svgImplicit Contentnicepng.com/downpng/u2w7a9e6w7e6i1u2_parental-advisory-implicit-contentMaria Agnesiupload.wikimedia.org/wikipedia/commons/5/57/Maria_Gaetana_Agnesi.jpgPortrait of Fermat by Roland Lefevre, public domainPortrait of Grandi, public domain.Clifford Truesdellen.wikipedia.org/wiki/Clifford_Truesdell#/media/File:Clifford_Truesdell.jpgPietro Fanfaniupload.wikimedia.org/wikipedia/commons/4/4c/Pietro_Fanfani.jpgJacopone da Todiupload.wikimedia.org/wikipedia/commons/0/0c/Paolo_Uccello_040.jpgGabriel Simeoniupload.wikimedia.org/wikipedia/commons/f/f0/Gabriel_Simeoni.pngIMAGE CREDITSCauchy Distributionupload.wikimedia.org/wikipedia/commons/4/47/CauchyVerteilung.PNGSolitoncommons.wikimedia.org/wiki/File:Soliton_hydro.jpgWitchesen.wikipedia.org/wiki/Witch_of_Agnesi#/media/File:Witch_of_Agnesi_curves.svgImplicit Contentnicepng.com/downpng/u2w7a9e6w7e6i1u2_parental-advisory-implicit-contentMaria Agnesiupload.wikimedia.org/wikipedia/commons/5/57/Maria_Gaetana_Agnesi.jpgPortrait of Fermat by Roland Lefevre, public domainPortrait of Grandi, public domain.Clifford Truesdellen.wikipedia.org/wiki/Clifford_Truesdell#/media/File:Clifford_Truesdell.jpgPietro Fanfaniupload.wikimedia.org/wikipedia/commons/4/4c/Pietro_Fanfani.jpgJacopone da Todiupload.wikimedia.org/wikipedia/commons/0/0c/Paolo_Uccello_040.jpgGabriel Simeoniupload.wikimedia.org/wikipedia/commons/f/f0/Gabriel_Simeoni.png⬣ MUSIC CREDITS ⬣"Night Watch" by Torus."Playfully" by V Draganov."Ursula Bones" by Roger Gabalda."Haunted House" by Danijel Zambo."Graveyard Tango" by Oliver Massa."Fairytales" by Danijel Zambo."Cautious Optimism" by Apex Music."The Air we Breathe" by Apex Music."Hostage" by Richard Bodgers.
Mathematician Deconstructs A Beautiful Mind Another Roof 2023-10-12 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣A Beautiful Mind tells the life story of John Nash. It features some mathematics, but how accurate is it? Join me as I break down these mathematical scenes to see if they hold up.⬣ TIMESTAMPS ⬣00:00 - Introduction01:51 - Game Theory05:51 - A Game Theory Application09:19 - Other Bits of Mathematics11:57 - Reviewing the Film⬣ CREDITS ⬣Music by Danjel Zambo.Intro Music by Aaron Paul Low.B-Footage Credits - Adapted for this video under Fair UseA Beautiful Mind © Universal Pictures, DreamWorks Pictures, Imagine Entertainment. Golden Balls © ITVDead Poets Society © Touchstone PicturesRadiolab interview: youtube.com/watch?v=vsgjBg0HqWQ&ab_channel=RadiolabAbel Prize presentation: youtube.com/watch?v=9At4Gfiw1qU&ab_channel=TheAbelPrizeImage CreditsNash with Nobel Prize, PBSwww-tc.pbs.org/wgbh/americanexperience/media/filer_public_thumbnails/filer_public/ee/8c/ee8c7650-3efc-4256-913a-ceaeefd2ecfa/nash-nobel-prize.jpg__2000x1448_q85_crop_subsampling-2_upscale.jpgNash with Abel Prizemedia.nj.com/njcom_photos/photo/2015/05/28/-987e17bac437ba25.JPGNick Corriganhttps://www.gov.wales/sites/default/files/campaign-case-studies/2022-11/Nick%20Corrigan%20960%20x%20450.jpgNash in Britannicacdn.britannica.com/55/199355-050-A5B77EDB/John-Nash-2007.jpgAbel Prize logoimages.squarespace-cdn.com/content/v1/5b769a490dbda32adeff7fa8/1534966743000-EUX26F1S7RISM3IRZKRE/4505ef52037243.59021c7e4dd33+copy.jpg?format=2500wNashupload.wikimedia.org/wikipedia/commons/9/91/John_f_nash_20061102_3.jpgJobs poster © Five Star Feature Filmshttps://m.media-amazon.com/images/M/MV5BMTM5NTQ3MTYxN15BMl5BanBnXkFtZTcwODE2Nzk3OQ@@._V1_.jpgSteve Jobs poster © Legendary Pictureshttps://i.ebayimg.com/images/g/EdYAAOSwmTtkpBGo/s-l1200.webpFirst Man poster © DreamWorks Picturesresizing.flixster.com/ZA8j-90Sc2neM-aO7a4C1rrSRTU=/ems.cHJkLWVtcy1hc3NldHMvbW92aWVzLzY1YmFmZmIwLWRmNmYtNGYyMS05OGRkLTNmYmE1ZGFhMTZjNi53ZWJwOppenheimer poster © Syncopy Incpbs.twimg.com/media/FYJtMnmVsAEEOnF?format=jpg&name=4096x4096Bohemian Rhapsody poster © 20th Century Foxhttps://m.media-amazon.com/images/M/MV5BMTA2NDc3Njg5NDVeQTJeQWpwZ15BbWU4MDc1NDcxNTUz._V1_.jpg
Why Do Sporadic Groups Exist? Another Roof 2023-09-27 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroofPermutation Group Visualiser by Tesseralis:permutation-groups.glitch.me⬣ ABOUT ⬣The concept of symmetry can be formalised through the study of groups. Groups can be constructed from simple groups, and during an incredible effort throughout the 20th century, all simple groups have been classified. But the classification is messy -- there are several infinite families and then 26 left-over groups which don't fit any of the patterns. In this video, we explore some of these so-called Sporadic Groups and why they exist.⬣ TIMESTAMPS ⬣00:00 - Intro and Housekeeping01:56 - Introduction to Group Theory05:13 - Classifying Groups10:04 - Transitive Groups15:06 - M2419:20 - The Mathieu Family26:29 - Why Sporadic Groups Exist⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ REFERENCES ⬣[1] É Mathieu, Sur la fonction cinq fois transitive de 24 quantitiés. Journal de mathématiques pures et appliquées 18 (1873) pp. 25-46.[2] E Witt, Die 5-fach transitiven Gruppen von Mathieu. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 12: 256–264[3] P Cameron, Projective and polar spaces. (1992) University of London, Queen Mary and Westfield College.[4] P Cameron, Permtation groups. (1999) London Mathematical Society Student Texts, Cambridge University Press.[5] W Burnside, Theory of Groups of Finite Order. (1911) Cambridge University P[6] mathshistory.st-andrews.ac.uk/Biographies/Mathieu_Emile[7] P Duhem, Emile Mathieu, his life and works. Bull. New York Math. Soc. 1(7): 156-168 (April 1892).[8] Aimo Tietäväinen, On the nonexistence of perfect codes over finite fields. SIAM Journal on Applied Mathematics, 24(1), 88–96.⬣ CREDITS ⬣Music by Danjel Zambo.Intro music by Tobias Voigt.Image CreditsMoleculecommons.wikimedia.org/wiki/File:Iridium_acetylacetonate_hydrate_complex_ball.pngPeriodic tableupload.wikimedia.org/wikipedia/en/7/76/Talk%2C_Periodic_table_%28demo_1%29.svgTesseracten.wikipedia.org/wiki/File:Tesseract.gifRingsmedia.distractify.com/brand-img/W01vvssml/1280x670/what-are-the-7-rings-of-power-1661952237955.jpegRackupload.wikimedia.org/wikipedia/commons/thumb/1/18/Torture_rack.jpg/1280px-Torture_rack.jpgMagmamedia.wired.co.uk/photos/606da0c989f3babb1f0133fb/master/w_1280,c_limit/Lava.jpgLatticestatic.buildeazy.com/wp-content/uploads/Depositphotos_10895998_ds-1024x1024.jpgKnot (quandle)https://math.illinois.edu/sites/default/files/inline-images/Fancy%20Knot-small.jpgErnst Witten.wikipedia.org/wiki/Ernst_Witt#/media/File:Ernst_Witt.jpegBernd Fischerupload.wikimedia.org/wikipedia/commons/3/36/Bernd_Fischer_MFO_2008.jpgRobert Griessupload.wikimedia.org/wikipedia/commons/3/3b/Robert_Griess.jpgFisher-Price Monstercoconuttoysandfancydress.com/ourshop/prod_7389206-FisherPrice-Giggles-n-Growls-Monster.htmlE8 Diagramupload.wikimedia.org/wikipedia/commons/1/14/E8Petrie.svgCircular arrowsfreepik.com/free-vector/recycling-circular-arrows-set_9650731.htmG2 Diagramen.wikipedia.org/wiki/G2_(mathematics)#/media/File:3-cube_t1.svgF4 Diagramen.wikipedia.org/wiki/F4_(mathematics)#/media/File:F4_roots_by_24-cell_duals.svgE6 Diagramen.wikipedia.org/wiki/E6_(mathematics)#/media/File:Up_1_22_t0_E6.svgE7 Diagramen.wikipedia.org/wiki/E7_(mathematics)#/media/File:Gosset_2_31_polytope.svgWilliam Burnsideupload.wikimedia.org/wikipedia/commons/8/8c/Burnside_2.jpegPlatonic Solidscommons.wikimedia.org/wiki/File:Platonic_solids.jpgExplosionvecteezy.com/video/2974313-explosion-on-green-screenExplosionyoutube.com/watch?v=Q7KmAe8_jZE&ab_channel=TimothyMillerSaturn, Jupiter timelapse, Voyager 1NASA Public Domain Image
The Hidden Geometry of Error-Free Communication Another Roof 2023-07-27 | Go to nordpass.com/anotherroof to get EXCLUSIVE access to NordPass’ best offer. It’s risk-free with a 30-day money-back guarantee! Or use my promo code anotherroof at checkout.Ask your questions for the Q&A here: reddit.com/r/anotherroof/comments/158a5he/31623_subscriber_qa_ask_your_questions_here⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬡ TWITCH: twitch.tv/anotherroof⬣ ABOUT ⬣The (extended) Golay code is a beautiful structure that has many practical uses and also rears its head in areas of pure mathematics. It makes for an efficient means of communicating across the vast distances in space, while also popping up in the study of sporadic simple groups.⬣ TIMESTAMPS ⬣00:00 - Introduction and Housekeeping03:52 - ISBN Error Detection07:00 - Hamming Codes, Error Correction, and Linearity19:45 - Weight and Distance in Linear Codes25:17 - Golay Code43:38 - Connection to S(5,8,24)49:03 - Outro⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ REFERENCES ⬣[1] E. R. Berlekamp. Key Papers in the Development of Coding Theory. IEEE Press (1974).[2] M. Golay. Notes on Digital Coding. Proc. IRE, vol 37, p657 (1949).[3] T. M. Thompson. From Error-Correcting Codes through Sphere Packings to Simple Groups, The Carus Mathematical Monographs (#21), Mathematical Association of America, pp. 16–17 (1983).⬣ CREDITS ⬣Music by Danjel Zambo.Brief excerpt from “Moon Men” by Jake Chudnow.Image CreditsElwyn Berlekampcommons.wikimedia.org/wiki/File:Elwyn_R_Berlekamp_2005.jpgPagercommons.wikimedia.org/wiki/File:Motorolapager.jpgVoyager 1NASA Public Domain ImageSporadic Groupscommons.wikimedia.org/wiki/File:SporadicGroups.svgSphere Packingcommons.wikimedia.org/wiki/File:Close-packed_spheres.jpgLIBRARIANNetFlix (fair use)Richard Hamminghttp://cm.bell-labs.com/cm/cs/alumni/hammingPunched Cardcommons.wikimedia.org/wiki/File:Used_Punchcard_(5151286161).jpgMarcel J. E. Golay (mathematician), Public Domainethw.org/w/images/e/e2/M._J._E._Golay.jpgMarcel Golay (astronomer), Public Domaincommons.wikimedia.org/wiki/File:Marcel_Golay_(Swiss_astronomer).jpgClaude Shannoncommons.wikimedia.org/wiki/File:ClaudeShannon_MFO3807.jpg
Maths Marathon: 24 Exams in 24 Hours (Part 3/3) Another Roof 2023-07-09 | ⬣ DONATE: tiltify.com/@anotherroof/maths-marathon-2023Any amount makes a difference, so please consider supporting! All money earned through super chats will go straight to Mind. Help me smash my target of £3000! Mental health is something I deeply care about so thank you in advance for supporting.
Maths Marathon: 24 Exams in 24 Hours (Part 2/3) Another Roof 2023-07-09 | ⬣ PART 3: youtube.com/live/7asekGBYIPY⬣ DONATE: tiltify.com/@anotherroof/maths-marathon-2023Any amount makes a difference, so please consider supporting! All money earned through super chats will go straight to Mind. Help me smash my target of £3000! Mental health is something I deeply care about so thank you in advance for supporting.
Maths Marathon: 24 Exams in 24 Hours (Part 1/3) Another Roof 2023-07-08 | ⬣ PART 2: youtube.com/live/9hN3zqHnXWU⬣ DONATE: tiltify.com/@anotherroof/maths-marathon-2023Any amount makes a difference, so please consider supporting! All money earned through super chats will go straight to Mind. Help me smash my target of £3000! Mental health is something I deeply care about so thank you in advance for supporting.
Why Am I Completing 24 Maths Exams in 24 Hours? Another Roof 2023-07-05 | ⬣ Please consider supporting Mind here:tiltify.com/@anotherroof/maths-marathon-2023Thank you!I'll update this description with links to the livestreams once I've set them up. I hope you enjoy!⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ TWITCH: twitch.tv/anotherroof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof
The Most Powerful Diagram in Mathematics Another Roof 2023-06-07 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ TWITCH: twitch.tv/anotherroof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroof⬣ ABOUT ⬣I have loved this diagram ever since I first saw it on the coffee cup of one of my lecturers / colleagues. But I was shocked to discover that its extraordinary properties weren’t very well-known! In this video, I build up some theory necessary to understand the MOG, then demonstrate how to use it.⬣ TIMESTAMPS ⬣00:00 - Intro02:49 - Motivation07:14 - Steiner Systems18:23 - Three Big Questions29:21 - S(5,8,24) and the MOG44:47 - Outro⬣ HINT ⬣Why might S(2,3,10) be impossible to construct? Try and prove the following lemma: If S(t,k,n) exists, then S(t-1,k-1,n-1) exists. Then use the contrapositive of this statement together with what we know about the number of blocks. In fact, one can prove that: If S(t,k,n) exists, then S(t-m,k-m,n-m) exists for integer m such that t-m is non-negative.⬣ INVESTIGATORS ⬣Nothing for you here. Sorry!⬣ REFERENCES ⬣R. T. Curtis, A New Combinatorial Approach to M24. Math. Proc. Camb. Phil. Soc. (1976), 79, 25.J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices, and Groups. Springer Science (1991).⬣ CREDITS ⬣Music by Danjel Zambo.Pythagorean Theorem diagram:upload.wikimedia.org/wikipedia/commons/d/d2/Pythagorean.svgJakob Steiner:upload.wikimedia.org/wikipedia/commons/5/55/JakobSteiner.jpgGino Fano:en.wikipedia.org/wiki/Gino_Fano
A Lifelong Mathematical Obsession Another Roof 2023-04-13 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroofContact me via my personal website if you’d like to hire me as a tutor:⬡ drmcgaw.co.uk⬣ ABOUT ⬣All my life, I have been obsessed with a counting puzzle I came up with as a child. Turns out, I’m not the first to think about it. Known as Hertzsprung’s Problem or the n-kings problem, I present an elementary proof of the general formula given by Morton Abramson and William Moser.⬣ TIMESTAMPS ⬣00:00:00 - Introduction and History00:11:04 - Overview00:17:14 - Stars & Bars 00:23:44 - Inclusion-Exclusion Principle00:29:31 - Pascal’s Triangle00:33:27 - Forbidden Pair Options Part 100:43:51 - Forbidden Pair Options Part 200:51:55 - Number of Permutations00:55:52 - Putting it all Together01:03:22 - A Cleaner Way?01:06:40 - Outro⬣ INVESTIGATORS ⬣Nothing for you in this one. Sorry!⬣ REFERENCES ⬣M Abramson and W Moser, Combinations, Successions and the n-Kings Problem. Mathematics Magazine, Vol. 39, No. 5 (Nov., 1966), pp. 269-273.⬣ CREDITS ⬣Music by Danjel Zambo.ImagesExplosion:vecteezy.com/video/2974313-explosion-on-green-screenHertzsprung-Russell Diagram, European Southern Observatory:commons.wikimedia.org/wiki/File:Hertzsprung-Russell_Diagram_-_ESO.pngEjnar Hertzsprung and Severin Hertzsprung are public domain.
Sherlock Holmes NEVER Deduced Anything Another Roof 2023-03-16 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroofContact me via my personal website if you’d like to hire me as a tutor:⬡ drmcgaw.co.uk⬣ ABOUT ⬣The word "deduction" is often used synonymously with "reach a conclusion." But deduction is much more specific than that. Watch to learn about the three types of reasoning -- deduction, induction, and abduction -- and find out which method Sherlock Holmes actually employs.⬣ TIMESTAMPS ⬣00:00 - Introduction03:13 - Deduction14:35 - Induction20:21 - Abduction26:03 - Conclusion⬣ INVESTIGATORS ⬣Slug is what Formal Alex is telling you. Don’t include spaces.⬣ CREDITS ⬣Music by Danjel Zambo.Ragtime music “Promenade Rag” by Giulio Fazio.Tick And Cross Vectors by Vecteezyvecteezy.com/free-vector/tick-and-crossLove Heart Vectors by Vecteezyvecteezy.com/free-vector/love-heartAnimal cell by domdomeggcommons.wikimedia.org/wiki/File:Simple_diagram_of_animal_cell_%28blank%29.svgNeuronfreesvg.org/neuronOsteocyte by OlafJanssencommons.wikimedia.org/wiki/File:Bone_cells_-_Osteocytes_3_--_Smart-Servier.pngBroken Heart Vectors by Vecteezyvecteezy.com/free-vector/broken-heartBlack Swan by JJ Harrisoncommons.wikimedia.org/wiki/File:Black_Swan_2_-_Pitt_Town_Lagoon.jpgSilent Film Border Vectors by Vecteezyvecteezy.com/free-vector/borderIncendies poster © Sony Pictures Classics.Prisoners poster © Warner Bros. Pictures.Enemy poster © A24.Sicario poster © Lionsgate.Arrival poster © Paramount Pictures.Blade Runner 2049 poster © Warner Bros. Pictures.Dune (2021) poster © Warner Bros. Pictures.Lock, Stock, and Two Smoking Barrels poster © Universal Pictures.Snatch poster © SKA Films.Swept Away poster © Screen Gems.Revolver poster © Redbus Film Distribution.RocknRolla poster © Warner Bros. Pictures.Sherlock Holmes poster © Warner Bros. Pictures.Sherlock Holmes: A Game of Shadows poster © Warner Bros. Pictures.The Man from U.N.C.L.E. poster © Warner Bros. Pictures.King Arthur: Legend of the Sword poster © Warner Bros. Pictures.Aladdin (2019) poster © Walt Disney Pictures.The Gentlemen poster © Miramax.Sherlock Footage and stills © BBCSherlock Holmes (2009) stills © Warner Bros. Pictures
Countdowns Most Impressive Solution: Explained #shorts Another Roof 2023-02-09 | From my video "The Surprising Maths of Britain's Oldest Game Show"Watch here: youtu.be/X-7Wev90lw4
What do you win on British game shows? #shorts Another Roof 2023-02-05 | From my video "The Surprising Maths of Britain's Oldest Game Show"Watch here: youtu.be/X-7Wev90lw4
A Simple Trick to Solve Countdown Numbers #shorts Another Roof 2023-02-01 | From my video "The Surprising Maths of Britain's Oldest Game Show"Watch here: youtu.be/X-7Wev90lw4
Whats the Hardest Target in Countdown? Another Roof 2023-01-28 | From my video "The Surprising Maths of Britain's Oldest Game Show"Watch here: youtu.be/X-7Wev90lw4
What Challenge did Descartes issue Fermat? #shorts Another Roof 2023-01-16 | From my video, "When Descartes Challenged Fermat (and Lost)."youtube.com/watch?v=xKfEmbWBgvM
If Classical Mathematicians Published Today #shorts Another Roof 2023-01-14 | From my video "When Descartes Challenged Fermat (and Lost)."youtube.com/watch?v=xKfEmbWBgvM
How did Fermat Inspire Newton? #shorts Another Roof 2023-01-12 | From my video "When Descartes Challenged Fermat (and Lost)."youtube.com/watch?v=xKfEmbWBgvM
Descartes Savage Responses to Critics #shorts Another Roof 2023-01-10 | From my video "When Descartes Challenged Fermat (and Lost)."youtube.com/watch?v=xKfEmbWBgvM
When Descartes Challenged Fermat (and Lost) Another Roof 2023-01-08 | ⬣ LINKS ⬣⬡ PATREON: patreon.com/anotherroof⬡ CHANNEL: youtube.com/c/AnotherRoof⬡ WEBSITE: https://anotherroof.top⬡ SUBREDDIT: reddit.com/r/anotherroofHow were tangents derived before calculus? And why did Descartes and Fermat, two of history’s more renowned mathematicians, hate each other? Watch to explore their methods to solve the tangent line problem and the origins of their bitter rivalry.Check out my series on building numbers from the ground up:youtube.com/playlist?list=PLsdeQ7TnWVm_EQG1rmb34ZBYe5ohrkL3t⬣ TIMESTAMPS ⬣Intro - 00:00Descartes and his Circle Method - 03:34Fermat and his Adequality Method - 15:13Rivalry - 29:09Folium of Descartes - 31:26Conclusion - 42:18Outro - 46:08⬣ CORRECTIONS ⬣In some sources, “Discourse on Method” is described as a work of three essays. Elsewhere, it is described as the introductory work to those three essays.⬣ INVESTIGATORS ⬣Are you still out there? Check my logic video for an update!⬣ REFERENCES ⬣[1] R. Descartes, La Geometrie, Trans. David Eugene Smith and Marcia L. Latham. Open Court Publishing Company: La Salle. (1952), pp. 95–112.[2] Selected Correspondence of Descartes, Jonathan Bennett 2017:earlymoderntexts.com/assets/pdfs/descartes1619.pdf[2a] to Mersenne, end of xii.1637, paraphrased.[2b] Fermat to Mersenne, iv or v 1637.[2c] to Morin, 13,vii.1638.[2d] to Mersenne 27.vii.1638 [2e] to Mersenne, ix.1641.[2f] against Fermat, 1.iii.1638.[2g] to Mersenne, 27.v.1638.[2h] to Mersenne, xii.1638.Huge thank you to Hal Hellman and his excellent “Great Feuds in Mathematics” for compiling many of the sources used in this video.[3] Hal Hellman, Great Feuds in Mathematics, 2006.[4] D. E. Smith, A Source Book in Mathematics, McGraw-Hill, 1929, pp. 389-96.[5] Fermat to Mersenne, December 1637; Fermat Oeuvres, vol. 2, p. 116. Translated by Daniel Curtin.[6] Fermat to Mersenne, February 1638; Fermat Oeuvres, vol. 2, pp. 132-33. Translated by Daniel Curtin.[7] G. F. Simmons, Calculus Gems, 1992 p. 101.[8] Fermat to Clerselier, March 10, 1658. Translated by elucidation by James Nicholson.[9] J. D. Nicholson, as detailed in Hal Hellman, "Great Feuds in Mathematics" 2006.[10] L. T. More, Isaac Newton, Scribner’s 1934 p. 185.⬣ CREDITS ⬣All music by Danjel Zambo.Images:Explosion: [vecteezy.com/free-png/fire-explosion] Fire Explosion PNGs by Vecteezy.Laser beams: [pngkit.com/view/u2t4i1w7e6i1o0e6_laser-beam-eyes-png]Sunglasses: [vecteezy.com/free-vector/meme-glasses] Meme Glasses Vectors by Vecteezy.
A Complex Number as Defined from the Axioms Another Roof 2022-12-23 | From my video on defining every number from the ZF axioms of set theory:youtube.com/watch?v=IzUw53h12wUCheck out the full series and my other videos here!youtube.com/anotherroof
How to Read Logic Another Roof 2022-11-13 | PATREON: patreon.com/anotherroofCHANNEL: youtube.com/c/AnotherRoofWEBSITE: https://anotherroof.topSUBREDDIT: reddit.com/r/anotherroofSymbolic logic looks intimidating, combining familiar symbols like equality and inclusion with lesser-known backwards E’s and upside down A’s. But with a bit of guidance, anyone can understand the meaning of these symbols and interpret logical statements.Check out my series on building numbers from the ground up:youtube.com/playlist?list=PLsdeQ7TnWVm_EQG1rmb34ZBYe5ohrkL3tTIMESTAMPS00:00 - Intro03:07 - Or, And, Not06:28 - Implication16:39 - Quantifiers26:26 - OutroINVESTIGATORSftfftttftf is not the slug you are looking for. CORRECTIONS*Propositions vs predicates: So that I didn’t overwhelm the viewer I stuck to just using “proposition” throughout. I know this isn’t strictly correct as many of the statements involving variables are actually prediates.**For some reason when recording I had it in my head that ‘n’ was a British thing when it is widely used throughout the Anglosphere and beyond.***Slip of the tongue that kind of undermines my point — the converse of Legrange’s Theorem would be “H is a subset with cardiality dividing |G| ⇒ H is a subgroup of G."****Another slip of the tongue that undermines the point — we are showing that whenever x is NOT zero, it has a reciprocal y=1/x.CREDITSAll music by Danjel Zambo.Octopus: freepik.com/free-vector/design-with-seamless-pattern-octopus_7033956.htm#query=octopus&position=7&from_view=search&track=sph Image by brgfx on FreepikPlatypus: freepik.com/free-vector/platypus-flat-cartoon-style_30758916.htm#query=playpus&position=19&from_view=search&track=ais Image by brgfx on FreepikHouse: freepik.com/free-photo/house-isolated-field_10025444.htm#query=house&position=1&from_view=search&track=sph Image by senivpetroon Freepik
Is 1 a Prime Number? Another Roof 2022-10-20 | PATREON: patreon.com/anotherroofCHANNEL: youtube.com/c/AnotherRoofWEBSITE: https://anotherroof.topSUBREDDIT: reddit.com/r/anotherroofCheck out my series on building numbers from the ground up:youtube.com/playlist?list=PLsdeQ7TnWVm_EQG1rmb34ZBYe5ohrkL3tOkay, we all know 1 isn’t prime. But it wasn’t always that way. It also wasn’t always considered to be a number at all. Join me on a deep dive into mathematical history to see how our concepts of numbers and primes changed over time.A huge thank you to my patrons for keeping the channel alive. Please consider supporting me by following the link above!An enormous thank you to Chris Caldwell et al. for their compilation of sources regarding the history of 1 as a prime. Their work is much more thorough and extensive than my video and covers many, many more examples of 1 defined as prime or otherwise. My video is intended as a rough narrative through line regarding the broad(ish) consensus regarding the status of 1. Having such an extensive list of sources was really helpful when writing. You can find their article here:Caldwell, Chris K. et al. “The History of the Primality of One: A Selection of Sources.” Journal of integer sequences 15.9 (2012).All music by Danijel Zambo.TIMESTAMPS:00:00 - Intro01:20 - Antiquity09:17 - Medieval13:50 - Modern23:59 - OutroREFERENCES[1] - Euclid. The Thirteen Books of The Elements, Vol. 2 Books III-IX. Translated by Heiberg. Dover Books on Mathematics, 1956.[2] - Martianus Capella. et al. Martianus Capella and the Seven Liberal Arts. Vol.2, The Marriage of Philology and Mercury. New York ;: Columbia University Press, 1977.[3] - Isidore, and Stephen A. Barney. The Etymologies of Isidore of Seville. Cambridge: Cambridge University Press, 2006.[4] - Khuwārizmĭ, Mu.hammad ibn Mūsá, Robert, and Barnabas. Hughes. Robert of Chester’s Latin translation of al-Khwārizmĭ’s al-Jabr : a new critical edition. Stuttgart: Franz Steiner, 1989.[5] - Stevin, S. The Principal Works of Simon Stevin. Vol.2B. Mathematics. C.V. Swets & Zeitlinger, 1958.[6] - Morland, Samuel. The Description and Use of Two Arithmetick Instruments : Together with a Short Treatise, Explaining and Demonstrating the Ordinary Operations of Arithmetick, as Likewise a Perpetual Almanack and Several Useful Tables : Presented to His Most Excellent Majesty Charles II ... London: Printed and are to be sold by Moses Pitt ..., 1673.[7] - Moxon, Joseph, and Henry Coley. Mathematicks Made Easie, or, A Mathematical Dictionary ... The second edition, corrected and much enlarged by Hen. Coley ... London: Printed for J. Moxon ..., 1692. [8] - Rahn, Johann Heinrich, Thomas Brancker, and John Pell. An Introduction to Algebra. London: Printed by W.G. for Moses Pitt ..., 1668. [9] - C. Goldbach, Letter to Euler dated 7 June 1742. Correspondance math´ematique et physique de quelques c´elebres geometres du XVIIIeme, siecle by P.-H. Fuss, Vol. I, pp. 125–129, Academie Imperiale des Sciences, St.-Petersbourg, 1843.[10] - J. G. Krüger, Gedancken von der Algebra, nebst den Primzahlen von 1 bis 1000000, Lüderwalds Buchhandlung, Halle, 1746. [11] - Euler, Leonhard, and John Hewlett. Elements of Algebra. Trans. John Hewlett. Cambridge: Cambridge University Press, 2009.[12] - Gauss, Carl Friedrich et al. Disquisitiones Arithmeticae. New York: Springer-Verlag, 1986. Print.[13] - Gregory, Olinthus. Mathematics for Practical Men : Being a Common-Place Book of Pure and Mixed Mathematics, Designed Chiefly for the Use of Civil Engineers, Architects and Surveyors. 4th ed / rev. and enl., by Henry Law. London: J. Weale, 1862.[14] - Hardy, G. H. (Godfrey Harold). A Course of Pure Mathematics. 6th ed. Cambridge Eng: The University Press, 1933.[15] - Hardy, G. H. (Godfrey Harold). A Course of Pure Mathematics. Centenary ed. Cambridge: Cambridge University Press, 2008. [16] - Sagan, C. Contact. Simon and Schuster, 1985.[17] - J. B. Andreasen, L.-A. T. Spalding, and E. Ortiz, FTCE: Elementary Education K-6, Cliffs Notes, Wiley, Hoboken, NJ, 2010.
Maths: Discovered or Invented? Do Computer-Aided Proofs Have Value? 10K Q&A Another Roof 2022-10-06 | Huge thank you to everyone who submitted questions -- this was a fun and relaxing video to make. Hopefully my views aren't too contentious.00:00 - Intro00:44 - Surreal Numbers?01:54 - Why YouTube?03:59 - Negative Bases?04:17 - Do I Make the Props?06:08 - Axiom of Choice?08:24 - Film, Music, Book?11:47 - Why Bricks?12:37 - How to Pronounce Gödel?13:12 - Favourite Theorem?17:17 - Do Computer-Assisted Proofs Have Value?21:10 - What's my PhD Thesis?23:37 - Favourite Type of Graph?24:12 - Channel Plans?24:57 - Favourite Number(s)?25:54 - Is Mathematics Invented or Discovered?29:10 - Outro
Defining Every Number Ever Another Roof 2022-09-26 | PATREON: patreon.com/anotherroofCHANNEL: youtube.com/c/AnotherRoofWEBSITE: https://anotherroof.topSUBREDDIT: reddit.com/r/anotherroofVisit my subreddit to ask questions — if I get enough I’ll make a 10K Q&A video.Previous videos!What are Numbers? youtu.be/dKtsjQtigagHow to Count: youtu.be/QO9a7h87DbAHow to Add: youtu.be/rhhhUAAAh-gOver my previous three videos, we defined the natural numbers 0, 1, 2, 3, and so on, then explored how to use them to count and carry out basic arithmetic. What about the negatives? Fractions? Irrationals? In this video we’ll develop our understanding of numbers to include all these and more.An enormous thank you to my Patrons. This one took me a while to make but you had my back every step of the way and encouraged me to take my time and make the video the best I can make it. If you'd like to support me and gain access to progress updates, bloopers, the Discord server where we can hang out, and have your name in the credits, please consider supporting me (link above)!NOTES: https://anotherroof.top/s/Video4Notes.pdfThis video is very long. Certain details had to be cut for the sake of pacing, but you can find some of those details in the notes above. You might also find other things of interest in there. I can confirm that everything you need is in the final portion of the video. And you'll need this:anotherroof.top/taking-adviceTimestamps:0:00:00 - Intro0:01:33 - The Plan0:03:33 - Preparation 1/3: New Axioms0:05:42 - Preparation 2/3: Cartesian Products0:10:49 - Preparation 3/3: Relations and Partitions0:22:39 - Short Break0:23:10 - Integers0:39:01 - Rationals0:55:10 - Real Numbers1:12:23 - Complex Numbers1:17:41 - Credits and Q&AComments and corrections:-There is some audio clipping in the video. Sorry about that. I tried a new microphone placement and only realised the issue long after shooting the whole video. Tried to fix it in post to no avail. Hopefully it isn’t too distracting!All music by Danijel Zambo.
How to Add Another Roof 2022-08-03 | Patreon: patreon.com/anotherroofChannel: youtube.com/c/AnotherRoofWebsite: https://anotherroof.topPrevious videos!What are numbers? youtu.be/dKtsjQtigagHow to count: youtu.be/QO9a7h87DbAAs previously explored, we can define the natural numbers in terms of sets. We can even use them to count. But how are operations like addition and multiplication defined? Along with a crash-course in proof by induction, we'll define these operations in this video and prove that they possess all the lovely properties with which we are familiar.Huge thank you to my Patrons. Without you, I wouldn't have the confidence to make YouTube part of my career may not have continued making videos. If you'd like to support me and gain access to progress updates, bloopers, the Discord server where we can hang out, and have your name in the credits, please consider supporting me (link above)!Join the subreddit! Thinking of doing a 10K subscriber Q&A video so head on over there and submit your questions, be they personal, mathematical, pedagogical, or whatever.Reddit: reddit.com/r/anotherroof00:00 - Intro04:02 - Axiom Recap05:28 - First Attempt at Addition09:05 - Addition Definition15:30 - Inductive Principle21:45 - Associativity of Addition25:25 - Commutativity of Addition30:30 - Multiplication Definition37:50 - Distributivity43:09 - Subtraction?44:25 - Closing Remarks*It is sufficient to define addition without the n+1:=S(n) part. However, I made the pedagogical choice to include this -- it's less efficient but more intuitive for the uninitiated, in my opinion.**The base cases of our inductions should deal with the n=0 case, as then the n=1 case is true by virtue of "true for k ⇒ true for (k+1)" where k=0. However, the n=0 case is always completely trivial so I decided to make my base cases at n=1 so that viewers less experienced with proof by induction get to see more "work" being done and get a feel for how to complete proofs by appealing to axioms. Let's just go ahead and assume we've proved the n=0 case separately in all proofs!***I misspeak here: We are proving that if a given number k commutes with *a* then the next number commutes with *a*. Apologies!****Psst, it's me, Yellow T-Shirt Alex, put the solution in the website slug. You'll also need those numbers I told you to keep safe!All music by Danijel Zambo.
How to Count Another Roof 2022-07-18 | Patreon: patreon.com/anotherroofChannel: youtube.com/c/AnotherRoofWebsite: https://anotherroof.topWatch the first video here! youtu.be/dKtsjQtigagHidden in this question is a lot of fascinating mathematics. Puzzle through and gain a greater appreciation for the simple act of counting. In this video, we will use our axioms to demonstrate how to construct functions and how we use them to robustly define counting. Last time, we defined the axioms of ZF and I highly recommend you watch that video first. Video making is something I’ve wanted to get into for a while.Solution is what you seek? Will you succeed? Need to grow my channel. You can help by sharing my videos. To all those who watched and shared my last video, thank you! Write to me through the link in my website to get in touch. Special thanks to all those who supported me on Buy Me a Coffee! Comment below with any feedback you think will improve my content.If you’d like to see more please consider supporting me on Patreon. Already, I’ve had lots of great feedback and really appreciate all the nice words. Solved — that’s how I’d like to feel about the video-making process but I’m not there yet. Try as I might, these videos take a really long time for me to make. Reverse engineering the mathematics to make it accessible to a wide audience is a slow process. Slug pace, some might say.00:00 - Intro01:28 - Motivation05:30 - Ordered Pairs17:51 - Functions20:56 - Thank You! And Patreon!21:36 - Function Types26:05 - Counting27:48 - Counting is Well-Defined36:45 - Closing Remarks*Correction: As stated, I show the 1-set, {{}}, where in fact I should show the 2-set {{},{{}}}.**I have no idea why my footage is so blurry from around the 26-minute mark. Apologies!All music by Danijel Zambo.
What IS a Number? As Explained by a Mathematician Another Roof 2022-06-29 | NEXT VIDEO IN SERIES youtube.com/watch?v=QO9a7h87DbASee how we develop even more concepts from this mathematical foundation.Ever wondered how numbers are actually defined? In this video, you'll learn the most common way it's done by mathematicians.MY PATREON IS NOW LIVE! Buy me a coffee if you like, but the best way to support me now is on Patreon, where I'll post updates, sneak peaks, bloopers, and my signing up you'll have your name in the credits of every video!Patreon: patreon.com/anotherroofBuy me a coffee: buymeacoffee.com/anotherroofChannel: youtube.com/channel/UCHEnZhUKjZSLYs3jJ0raKZAWebsite: https://anotherroof.topMy website may be a good place to start if you're confused...#SoME200:00 - Intro02:19 - Motivation04:12 - Physical Units: An Analogy08:26 - First Attempt10:39 - The Perils of Intuition12:40 - Definition in Principle15:38 - Sets and Russell's Paradox23:44 - Rules of Sets31:46 - Constructing the Numbers38:25 - Cake38:29 - Closing Remarks*Galileo's Paradox: In his final book, which bears the catchy title, "...," Galileo discusses the size of the set of natural numbers versus that of the set of square numbers (not even numbers, as in my video, but the point is the same). It's written as a dialogue, not as a letter as I erroneously claimed.**Formulations of ZF: There are several equivalent ways of formulating ZF set theory. Some have that the empty set exists as an axiom, but not all. Others prove the existence of the empty set by using the axiom of infinity then the axiom of subsets, and others argue similarly to how I argue in that in first-order logic, something exists. The point is, I shouldn't have claimed that the axiom of the empty set is always part of ZF.ImagesIPK:upload.wikimedia.org/wikipedia/commons/e/e1/International_prototype_of_the_kilogram_aka_Le_Grand_K.jpgPrototype metre bars:cdn2.picryl.com/photo/1969/12/31/platinum-iridium-meter-bar-a79c8f-1024.jpgAll music by Danijel Zambo.
Maths Teacher Does 24 Exams in 24 Hours (Part 3/3) Another Roof 2022-04-10 | Donate here: tiltify.com/@drmcgaw/maths-marathon-24-exams-in-24-hoursAll support is appreciated. Help me on my maths mission to raise £2000 for Refuge, a charity providing support for victims of domestic violence. I'm a UK-based maths teacher and PhD graduate. Lockdown was relatively easy for me but hell for many. If you are unable to give, please enjoy the show, ask a question in the comments, and share!
Maths Teacher Does 24 Exams in 24 Hours (Part 2/3) Another Roof 2022-04-10 | PART 3 HERE: youtu.be/q4zWF0QpczgDonate here: tiltify.com/@drmcgaw/maths-marathon-24-exams-in-24-hoursAll support is appreciated. Help me on my maths mission to raise £2000 for Refuge, a charity providing support for victims of domestic violence. I'm a UK-based maths teacher and PhD graduate. Lockdown was relatively easy for me but hell for many. If you are unable to give, please enjoy the show, ask a question in the comments, and share!
Maths Teacher Does 24 Exams in 24 Hours (Part 1/3) Another Roof 2022-04-09 | PART 2 HERE: youtu.be/T9h55waUth8 Donate here: tiltify.com/@drmcgaw/maths-marathon-24-exams-in-24-hoursAll support is appreciated. Help me on my maths mission to raise £2000 for Refuge, a charity providing support for victims of domestic violence. I'm a UK-based maths teacher and PhD graduate. Lockdown was relatively easy for me but hell for many. If you are unable to give, please enjoy the show, ask a question in the comments, and share!
