Poncelet’s Porism – Numberphile

From Numberphile. Featuring Daniel Litt. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Daniel Litt: https://www.daniellitt.com/ See Daniel previously on Numberphile: https://youtu.be/eYfpSAxGakI Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation…

Predators and Prey – Numberphile

From Numberphile. Tom Crawford talks foxes and rabbits. More links & stuff in full description below ↓↓↓ More of Tom on Numberphile: http://bit.ly/TomPlaylist Tom’s website: https://tomrocksmaths.com Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process…

How did Ramanujan solve the STRAND puzzle?

From Mathologer. Today’s video is about making sense of an infinite fraction that pops up in an anecdote about the Indian mathematical genius Srinivasa Ramanujan. 00:00 Intro 04:31 Chapter 1: Getting a feel for the puzzle 08:27 Chapter 2: Algebra autopilot 12:37 Chapter 3: Infinite fraction 17:51 Chapter 4: Root 2 21:19 Chapter 5: Euclidean…

Why is there no equation for the perimeter of an ellipse‽

From Standup Mathematician. Applications for paid internships at Jane Street are open! https://www.janestreet.com/join-jane-street/internships/ A Podcast of Unnecessary Detail is out now: https://festivalofthespokennerd.com/podcast/ Come for the Unnecessary Detail, stay for the A Podcast Of. These are my approximation equations: perimeter ≈ π[53a/3 + 717b/35 – √(269a^2 + 667ab + 371b^2)] perimeter ≈ π(6a/5 + 3b/4) If…

Hamming codes part 2, the elegance of it all

From 3Blue1Brown. Part 1: https://youtu.be/X8jsijhllIA Watch Ben Eater’s video: https://youtu.be/h0jloehRKas Viewer-supported: https://3b1b.co/hamming-thanks A cleaner perspective on Hamming error correction codes. You can read Hamming’s own perspective on his discovery of these codes in chapter 12 of "The Art of Doing Science and Engineering". https://amzn.to/3lwcnmh Heavily related is the chessboard puzzle I did with Matt Parker:…

Hamming codes, h■w to ov■rco■e n■ise.

From 3Blue1Brown. A discovery-oriented introduction to error correction codes. Part 2: https://youtu.be/b3NxrZOu_CE Ben Eater:’s take: https://youtu.be/h0jloehRKas Viewer-supported: https://3b1b.co/hamming-thanks Heavily related is the chessboard puzzle I did with Matt Parker: https://youtu.be/as7Gkm7Y7h4 You can read Hamming’s own perspective on his discovery of these codes in chapter 12 of "The Art of Doing Science and Engineering". https://amzn.to/3lwcnmh The…

Landmark Numbers and Bad Number Analogies

From Standup Mathematician. You can pre-order Tim’s book How to Make the World Add Up now! https://mathsgear.co.uk/products/how-to-make-the-world-add-up-signed-hardback Watch Tim Harford talk about the Stork-Baby correlation on Numberphile: https://www.youtube.com/watch?v=-n-d1ApBTFw Here is the current Landmark Number recommended toolkit (yours may differ). – population of the country you live in – ‘people days’ per year in your countries…

The Brussels Choice – Numberphile

From Numberphile. Neil Sloane from the OEIS discusses the Choix de Bruxelles. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Neil Sloane founded the runs the OEIS: https://oeis.org/ Brussels Choice on the OEIS: https://oeis.org/A323454 Neil Sloane playlist on Numberphile: http://bit.ly/Sloane_Numberphile Neil Sloane on…

What is the biggest tangent of a prime?

From Standup Mathematician. What is your Mega-Favourite Number? The playlist of #MegaFavNumbers videos is here: https://www.youtube.com/watch?v=R2eQVqdUQLI&list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo If you make a video about a number bigger than 1,000,000 use the hashtag #MegaFavNumbers and we’ll add it to the playlist! Here is my current mega-favourite number: 1,169,809,367,327,212,570,704,813,632,106,852,886,389,036,911 This is the OEIS page for A249836: Numbers n for…

Group theory and why I love 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000

From 3Blue1Brown. An introduction to group theory, and the monster group. Paid for by viewers, like you: https://3b1b.co/monster-thanks Minor error corrections below↓↓↓ This video is part of the #MegaFavNumbers project: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo To join the gang, upload your own video on your own favorite number over 1,000,000 with the hashtag #MegaFavNumbers, and the word MegaFavNumbers in…

Does “land area” assume a country is perfectly flat?

From Standup Mathematician. You can listen to the A Problem Squared podcast here (and everywhere else). Please do! https://aproblemsquared.libsyn.com/ Huge thanks to Dr Laura Graham! Everything they did is on github: https://github.com/laurajanegraham/surface_area/blob/master/surface_area.md All about Laura: https://laurajanegraham.github.io/ Prof Alasdair Rae was also big help and sent me their slides. http://bit.ly/measurelandarea This is that video: https://www.youtube.com/watch?v=pDYkiK90WCM All…

Squares and Tilings – Numberphile

From Numberphile. With 2006 Fields Medallist Andrei Okounkov More links & stuff in full description below ↓↓↓ Professor Okounkov website: http://www.math.columbia.edu/~okounkov/ Numberphile Field Medallist Playlist: https://bit.ly/Fields_Playlist Roger Penrose on the Numberphile Podcast: https://youtu.be/JiDWGbsVEno Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative…

Dungeon Numbers – Numberphile

From Numberphile. Featuring Neil Sloane from the OEIS. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor)… More links & stuff in full description below ↓↓↓ Part 2: https://youtu.be/HFeKdMf01rQ Neil Sloane is the founder of the The On-Line Encyclopedia of Integer Sequences. Visit it here: https://oeis.org More Neil Sloane on Numberphile: http://bit.ly/Sloane_Numberphile Numberphile…

Ellipsoids and The Bizarre Behaviour of Rotating Bodies

From Standup Mathematician. Derek’s video: The Bizarre Behavior of Rotating Bodies, Explained https://www.youtube.com/watch?v=1VPfZ_XzisU Based on this amazing footage: Dancing T-handle in zero-g https://www.youtube.com/watch?v=1n-HMSCDYtM Terence Tao’s original answer, with update. https://mathoverflow.net/questions/81960/the-dzhanibekov-effect-an-exercise-in-mechanics-or-fiction-explain-mathemat Support me on Patreon and I can make more video like this! https://www.patreon.com/standupmaths We are sat so close because we filmed this in the “before…

Hat Problems – Numberphile

From Numberphile. Featuring Joe Buhler. See part 2 of this interview: https://youtu.be/4YG4QnhVV7A More links & stuff in full description below ↓↓↓ An Introduction to Infinite Hat Problems (paper): https://bit.ly/31OeWZK See also Spheres and Code Words with James Grime: https://youtu.be/T46FTuHnbvY Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by…

The impossible chessboard puzzle

From 3Blue1Brown. An information puzzle with an interesting twist Solution on Stand-up Maths: https://youtu.be/as7Gkm7Y7h4 Paid for by viewers, like you: https://3b1b.co/chess-thanks Home page: https://www.3blue1brown.com —————— 0:00 Introduction 3:58 Visualizing the two-square case 5:46 Visualizing the three-square case 12:19 Proof that it’s impossible 16:22 Explicit painting of the hypercube —————— Thanks to everyone who endured me…

Complex Fibonacci Numbers?

From Standup Mathematician. Huge thanks to Jane Street! https://www.janestreet.com/join-jane-street/ Check out Ben Sparks’s GeoGebra files. Binet formula 2D complex output: https://www.geogebra.org/m/twvvzpga 3D imaginary output of Binet formula: https://www.geogebra.org/m/z6dy9cj5 3D plot of absolute output of Binet formula: https://www.geogebra.org/m/pb7hmxyd My four-part series on Numberphile videos about Fibonacci Numbers (from 2014) starts here. https://www.youtube.com/watch?v=D8ntDpBm6Ok Here is me going…

What is the best way to lace your shoes? Dream proof.

From Mathologer. A blast from the past. A video about my fun quest to pin down the best ways of lacing mathematical shoes from almost 20 years ago. Lots of pretty and accessible math. Includes a proof that came to me in a dream (and that actually worked)! 0:00 Intro 1:31 What’s a mathematical lacing?…

Beautiful Trigonometry – Numberphile

From Numberphile. Featuring Ben Sparks. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Catch a more in-depth interview with Ben on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk Ben’s website: https://www.bensparks.co.uk More Numberphile videos with Ben Sparks: http://bit.ly/Sparks_Playlist Explore this topic further with this Geogebra file…

The Stack Folding Challenge

From Standup Mathematician. AHGD / BCFE AHBG / DECF The "Stack Folding Challenge" is to fold the two lay-outs I show in the video. But the MPMP meta-puzzle is to work out how many different Stack Folding Challenges are possible. That is to say: how many ways can you fold such a piece of paper…

A Surprising Pi and 5 – Numberphile

From Numberphile. Ben Sparks discusses 5 and Pi. Catch a more in-depth interview with Ben on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Ben’s website: https://www.bensparks.co.uk More Numberphile videos with Ben Sparks: http://bit.ly/Sparks_Playlist Catch Ben on the latest…

Tips to be a better problem solver [Last lecture] | Lockdown math ep. 10

From 3Blue1Brown. Tips on problem-solving, with examples from geometry, trig, and probability. Past episodes with integrated quizzes: https://itempool.com/c/3b1b Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Huge huge thanks to Ben Eater: https://www.youtube.com/user/eaterbc And Cam Christensen, creator of ItemPool: https://itempool.com/ Notes by Ngân Vũ: https://twitter.com/ThuyNganVu/status/1265480770832855040 Mistakes: 50:35, there should be a…

Are Matt and James anti-psychic?

From Standup Mathematician. Yes, technically we’re "NAND psychic". Want to own Matt’s red/black sign, signed by him and James? It’s being auctioned for charity: https://www.ebay.co.uk/itm/362997607146 James’s Singing Banana channel is over here: https://www.youtube.com/user/singingbanana Here is our previous collaboration: "The Difference of Two Squares" https://www.youtube.com/watch?v=LkIK8f4yvOU Want to watch the full unedited footage of us being anti-psychic?…

Matrix Factorization – Numberphile

From Numberphile. Featuring Professor David Eisenbud, director of the Mathematical Sciences Research Institute (MSRI). More links & stuff in full description below ↓↓↓ More videos with Professor Eisenbud: http://bit.ly/Eisenbud_Videos More form the Professor on our podcast: https://youtu.be/9y1BGvnTyQA The 17-gon: https://youtu.be/87uo2TPrsl8 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported…

Intuition for i to the power i | Lockdown math ep. 9

From 3Blue1Brown. i^i, visualized and explained. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Mistakes: At 1:06:20, when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct. It’s what we’d think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i)…

Does contact tracing necessarily sacrifice privacy? (via Nicky Case)

From 3Blue1Brown. Though many contact tracing apps involve location tracking, they don’t have to. This is a video adaptation of a post by Nicky Case: https://ncase.me/contact-tracing/ New post by Nicky on COVID-19: https://ncase.me/covid-19/ Consider supporting his work: https://www.patreon.com/ncase/ Supporters of this video: https://3b1b.co/ctracing-thanks DP-3T Whitepaper: https://github.com/DP-3T/documents/blob/master/DP3T%20White%20Paper.pdf Full repo: https://github.com/DP-3T Where did the number 60% come…

The power tower puzzle | Lockdown math ep. 8

From 3Blue1Brown. A fun puzzle stemming from repeated exponentiation. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Notes by Ngân Vũ: https://twitter.com/ThuyNganVu/status/1261014161464516608?s=20 Play along on Desmos: https://www.desmos.com/calculator/nul32eaaa9 Related videos. Calculus series: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr In particular look at: https://youtu.be/CfW845LNObM Numberphile on Grahm’s constant: https://youtu.be/XTeJ64KD5cg —————— Video timeline (thanks to user "noonesperfect") 0:36 Question…

What makes the natural log “natural”? | Lockdown math ep. 7

From 3Blue1Brown. All about ln(x). Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1259288683489849344 Errors: At minute 16, the sum should be written with a "…" to indicate going to infinity. At minute 38, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent…

Euler Squares – Numberphile

From Numberphile. Also known as Graeco-Latin Squares. Featuring Dr James Grime. Extra footage at: https://youtu.be/HuIrUeODtVQ Patreon: http://www.patreon.com/numberphile More links & stuff in full description below ↓↓↓ Dr James Grime’s website: https://www.singingbanana.com More James Grime videos on Numberphile: http://bit.ly/grimevideos This video was coincidentally released the day of this news: https://www.news18.com/news/opinion/indian-maths-genius-who-debunked-eulers-theory-made-it-to-nyc-front-page-dies-at-103-2611193.html  Numberphile is supported by the Mathematical…

Logarithm Fundamentals | Lockdown math ep. 6

From 3Blue1Brown. Back to the basics with logarithms. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Triangle of power: https://youtu.be/sULa9Lc4pck Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258222677573001219 —————— The live question setup with stats on-screen is powered by Itempool. https://itempool.com/ Curious about other animations? https://www.3blue1brown.com/faq#manim Music by Vincent Rubinetti. Download the music…

Euler’s crazy pi formula generator

From Mathologer. Today we derive them all, the most famous infinite pi formulas: The Leibniz-Madhava formula for pi, John Wallis’s infinite product formula, Lord Brouncker’s infinite fraction formula, Euler’s Basel formula and it’s infinitely many cousins. And we do this starting with one of Euler’s crazy strokes of genius, his infinite product formula for the…

Imaginary interest rates | Lockdown math ep. 5

From 3Blue1Brown. Compound interest, e, and how it relates to circles. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Great Mathologer video: https://youtu.be/-dhHrg-KbJ0 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258221677990703105 https://twitter.com/ThuyNganVu/status/1258222002889875457 My other videos on imaginary exponents: https://youtu.be/v0YEaeIClKY https://youtu.be/mvmuCPvRoWQ Mistakes: In the off-handed remarks on quaternions, I mentioned rotation in 4d would…

What is Euler’s formula actually saying? | Lockdown math ep. 4

From 3Blue1Brown. What does it mean to compute e^{pi i}? Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258220129327800320 https://twitter.com/ThuyNganVu/status/1258220541686628353 —————— Video Timeline (Thanks to user "Just TIEriffic") 0:00:00 Welcome 0:00:20 Ending Animation Preview 0:01:15 Reminders from previous lecture 0:03:30 Q1: Prompt (Relationship with e^iθ=…) 0:05:40…

The 1890 US Census and the history of punchcard computing [feat. Grant of 3blue1brown fame]

From Standup Mathematician. Thanks to Grant Sanderson (of 3blue1brown fame) for joining me on a fun day out! Best double-check you are definitely subscribed to their channel: https://www.youtube.com/3blue1brown If you are ever in the Bay Area you should totally check out the Computer History Museum. https://computerhistory.org/ Bubbles Whiting – Using Punch Cards – Hollerith and…

Lewis Carroll’s Pillow Problem – Numberphile

From Numberphile. Featuring Alex Bellos. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More videos with Alex Bellos: http://bit.ly/Bellos_Playlist Alex’s website: http://www.alexbellos.com And his books on Amazon (including "So You Think You’ve Got Problems" in which this puzzle features): https://amzn.to/3cRViyf and https://amzn.to/2xfDUUZ Monty…

Complex number fundamentals | Lockdown math ep. 3

From 3Blue1Brown. Intro to the geometry complex numbers. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258219199769440257 Errors: – On the first sketch of a complex plane, there is a "2i" written instead of "-2i". – At the end, in writing the angle sum identity, the…

The Parker Machine: it’s 80% accurate.

From Standup Mathematician. Check out the full lecture on the Royal Institution YouTube channel. https://www.youtube.com/watch?v=_q4DrUHKC0Q Ri Christmas Lectures thanks to: The BBC – https://www.bbc.co.uk/programmes/m000crbc The Royal Institution – https://www.rigb.org/christmas-lectures/2019-secrets-and-lies Windfall Films – http://www.windfallfilms.com/show/1054/royal-institution-christmas-lectures.aspx Directed by David Coleman, produced by Laura Voak. Bonus footage filmed and edited by Matt Parker CORRECTIONS – Nothing yet. Let me…

Trigonometry fundamentals | Lockdown math ep. 2

From 3Blue1Brown. Intro to trig with a lurking mystery about cos(x)^2 Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks —————– Contents: Introduction  – 0:00 Q1 Graph of (cos θ)²  – 2:14 Q2 Translations of cos θ to (cos θ)²  – 5:34 Q3 f(2x) = f(x)²  – 10:54 Intro to Trig  – 13:14 Q4 sin(3) & cos(3)  –…

Why is this Puzzle Impossible? – Numberphile

From Numberphile. Don’t try this at home – it’s impossible… Professor Steven Bradlow explains. More links & stuff in full description below ↓↓↓ Steven Bradlow: https://math.illinois.edu/directory/profile/bradlow Buy the puzzle on Amazon (affiliate link): https://amzn.to/2yt8MBA Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation…

The simpler quadratic formula | Lockdown math ep. 1

From 3Blue1Brown. Another view on the quadratic formula. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258217451323416577 Po Shen Loh on quadratics: https://www.youtube.com/watch?v=ZBalWWHYFQc Welch Labs on imaginary numbers: https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF Mistakes (there will always be mistakes): At minute 22, I write "b’ / 2" instead of "-b’…

The Daddy of Big Numbers (Rayo’s Number) – Numberphile

From Numberphile. Professor Tony Padilla is back with another epic number. Our Big Number playlist of previous videos: http://bit.ly/Big_Numbers More links & stuff in full description below ↓↓↓ Busy Beavers on Computerphile: https://youtu.be/CE8UhcyJS0I With thanks to Agustín Rayo himself. Read more from Prof Rayo at: http://web.mit.edu/arayo/www/bignums.html And see his website at: https://arayo.scripts.mit.edu/home/ Tony Padilla: https://twitter.com/DrTonyPadilla…

Impossible Squares – Numberphile

From Numberphile. Ben Sparks shows us a simple problem that takes some fascinating twists. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More videos with Ben Sparks: http://bit.ly/Sparks_Playlist Catch a more in-depth interview with Ben on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk Ben’s website: https://www.bensparks.co.uk…