The Dehn Invariant – Numberphile

From Numberphile. It was #3 on Hilbert’s list of the most important problems in mathematics – until his student solved it. More links & stuff in full description below ↓↓↓ Featuring Daniel Litt, currently at the Institute for Advanced Study – https://twitter.com/littmath David Hilbert’s problems: https://en.wikipedia.org/wiki/Hilbert%27s_problems Max Dehn’s famed proof: https://archive.org/details/mathematischean33behngoog/page/n488 Numberphile is supported by…

Understanding e to the i pi in 3.14 minutes | DE5

From 3Blue1Brown. Euler’s formula intuition from relating velocities to positions. Home page: https://www.3blue1brown.com Yeah yeah, the runtime is 4:08, but it’s 3.14 minutes to the conclusion. Not familiar with the calculus referenced in this video? Try taking a look at this one: https://youtu.be/m2MIpDrF7Es Another perspective on this formula, from Mathologer: https://youtu.be/-dhHrg-KbJ0 Another perspective from this…

But what is a Fourier series? From heat flow to circle drawings | DE4

From 3Blue1Brown. Fourier series, from the heat equation to sines to cycles. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de4thanks Thanks to Stuart@Biocinematics for the one-line sketch of Fourier via twitter. As it happens, he also has an educational YouTube channel: https://www.youtube.com/channel/UCKOiJd9YCbv7LeL2LFOGiLQ Small correction: at 9:33, all the exponents should have a pi^2 in…

Necklace Splitting (a lesson for jewel thieves) – Numberphile

From Numberphile. Featuring Professor Noga Alon. More links & stuff in full description below ↓↓↓ Extra footage: https://youtu.be/E-8YvnaumKU Recorded with Noga Alon at Princeton University. Read his necklace paper: https://m.tau.ac.il/~nogaa/PDFS/Publications2/Splitting%20necklaces.pdf Diamond on Periodic Videos: https://youtu.be/EmXe5EDQvsg Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons…

Solving the heat equation | DE3

From 3Blue1Brown. Boundary conditions, and setup for how Fourier series are useful. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de3thanks More about the heat equation, with a derivation in terms of slope corresponding to heat flow from MIT OCW: https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf If you want to learn more about Fourier series, here are a few great…

What’s the story with log(1 + 2 + 3)?

From Standup Mathematician. This is my deep dive into the log(1 + 2 + 3) = log(1) + log(2) + log(3) log troll meme. I’m not going to link to any of the online discussions incase I accidentally encourage brigading. If you want to join in constructively, you can google them. Huge thanks to Jane…

Don’t Know (the Van Eck Sequence) – Numberphile

From Numberphile. Neil Sloane on the Van Eck Sequence… Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More Neil Sloane: http://bit.ly/Sloane_Numberphile Van Eck sequence on OEIS: https://oeis.org/A181391 Afraid So is by Jeanne Marie Beaumont Numberphile is supported by the Mathematical Sciences Research Institute…

Tribonacci Numbers (and the Rauzy Fractal) – Numberphile

From Numberphile. Edmund Harriss introduces a very cool tiling and talks about Tribonacci Numbers. More links & stuff in full description below ↓↓↓ Numberphile Podcast: https://www.numberphile.com/podcast Or on YouTube: http://bit.ly/Numberphile_Pod_Playlist More Edmund on Numberphile: http://bit.ly/Ed_Harriss_Playlist Ed Harriss is online at http://maxwelldemon.com and on Twitter at https://twitter.com/gelada Papers relating to this video… Nombres algébriques et substitutions:…

Calculator Number Trick: rectangle patterns

From Standup Mathematician. Here is the original Fermat’s Library tweet. https://twitter.com/fermatslibrary/status/1052544515632959488 If you want 100% renewable energy: check out Bulb! https://bulb.co.uk/refer/mattp5449 We make Think Maths teaching resources to go with Stand-up Maths videos. For this one we have a cheat sheet to an algebraic proof. http://think-maths.co.uk/standupmaths-videos?yt-calculator-rectangles#calculator-rectangles Many people are asking for the gif. It’s available…

Game of Cat and Mouse – Numberphile

From Numberphile. Ben Sparks discusses the math behind a curious problem…. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Worst Mouse Ever merch (including T-Shirt): https://teespring.com/worst-mouse-ever-numberphile Circling Tactic merch: https://teespring.com/circling-tactic More videos with Ben Sparks: http://bit.ly/Sparks_Playlist Ben’s own website: https://www.bensparks.co.uk Animation with GeoGebra:…

Recursive PowerPoint Presentations [Gone Fractal!]

From Standup Mathematician. Thanks to Steve Mould for filming with me. Check out his “How viruses self assemble” video. https://youtu.be/3X6qEE2fHvE We have since made the t-shirt I’m wearing available for purchase: https://fotsn.teemill.com/collection/recursive-t-shirt/ We have some free teaching resources for anyone who wants to make a large collaborative fractal! As well as complicated 3D ones we’ve…

Will your name become extinct? – Numberphile

From Numberphile. Dr James Grime discusses the mathematics of extinction. More links & stuff in full description below ↓↓↓ Extras from this interview: https://youtu.be/zomuAufWXr0 Related but different video on the math of ancestry: https://youtu.be/Fm0hOex4psA More James Grime videos: http://bit.ly/grimevideos James Grime: https://www.singingbanana.com Dice videos: http://bit.ly/Dice_Videos Thanks to the AP Archive: http://www.aparchive.com and https://youtube.com/channel/UCHTK-2W11Vh1V4uwofOfR4w Numberphile is…

EVERY baby is a ROYAL baby – Numberphile

From Numberphile. Dr James Grime discusses ancestry and why we ALL have royal blood. See also our new video on family extinction at: https://youtu.be/z34XhE5oRwo More links & stuff in full description below ↓↓↓ More James Grime videos: http://bit.ly/grimevideos #RoyalBaby James Grime: https://www.singingbanana.com Additional reading on this topic: http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-Article.pdf Numberphile is supported by the Mathematical…

Solving EQUATIONS by shooting TURTLES with LASERS

From Mathologer. Today’s video is about Lill’s method, an unexpectedly simple and highly visual way of finding solutions of polynomial equations (using turtles and lasers). After introducing the method I focus on a couple of stunning applications: pretty ways to solve quadratic equations with ruler and compass and cubic equations with origami, Horner’s form, synthetic…

A final game with Elwyn Berlekamp (Amazons) – Numberphile

From Numberphile. The legendary Elwyn Berlekamp died on April 9, 2019. In a final filming session with Numberphile, the games expert taught us how to play Amazons. More links in full description below ↓↓↓ Extras from this interview: https://youtu.be/mTl7W18UwFM Dots & Boxes with Elwyn: https://www.youtube.com/watch?v=KboGyIilP6k Elwyn’s own video on Amazons: https://youtu.be/_1NzUMWeU4c Elwyn obituary in Berkeley…

But what is a partial differential equation? | DE2

From 3Blue1Brown. The heat equation, as an introductory PDE. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de2thanks Infinite powers, by Steven Strogatz: https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Universe/dp/1328879984 Typo corrections: – At 1:33, it should be “Black-Scholes” – At 16:21 it should read “scratch an itch”. If anyone asks, I purposefully leave at least one typo in each video,…

What’s so special about the Mandelbrot Set? – Numberphile

From Numberphile. Featuring Ben Sparks discussing the Mandelbrot Set (and Julia Sets). More links & stuff in full description below ↓↓↓ More videos with Ben: http://bit.ly/Sparks_Playlist Ben Sparks website: https://www.bensparks.co.uk And on Twitter: https://twitter.com/sparksmaths Holly Krieger has done a few Mandelbrot videos on Numberphile… The Mandelbrot Set: https://youtu.be/NGMRB4O922I 63 and -7/4 are special: https://youtu.be/09JslnY7W_k Pi…

How many ways can circles overlap? – Numberphile

From Numberphile. T-shirt and poster details below. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Featuring Neil Sloane from the OEIS: https://oeis.org And thanks to Jonathan Wild: https://www.mcgill.ca/music/jonathan-wild OEIS A250001 – Number of arrangements of n circles in the affine plane: https://oeis.org/A250001 3-Circles…

Why didn’t GPS crash?

From Standup Mathematician. More on the GPS roll-over. https://www.theregister.co.uk/2019/02/12/current_gps_epoch_ends/ “In the Future the Modernized GPS Navigation (CNAV and MNAV) message has a 13-bit week number, which for all practical purposes solves this ambiguity” https://www.gps.gov/cgsic/meetings/2017/powers.pdf See me turn on my TomTom: https://www.patreon.com/posts/26065751 If you want to see more hilarious tales about roll-over errors then, well, READ…

90,525,801,730 Cannon Balls – Numberphile

From Numberphile. Matt Parker has a new favourite number – again! More links & stuff in full description below ↓↓↓ Some notes from Matt on how far he has investigated: https://www.numberphile.com/cannon-ball-numbers Matt’s book “Humble Pi” via Maths Gear (signed and ships almost everywhere): http://bit.ly/Humble_Pi More Numberphile videos with Matt: http://bit.ly/Matt_Videos James Grime sphere packing: https://youtu.be/CROeIGfr3gs…

When Buildings Wobble: with Paul Shepherd

From Standup Mathematician. Watch the whole lecture on the Ri channel: https://www.youtube.com/watch?v=6JwEYamjXpA You can buy my book now! Get it from Maths Gear and I’ll totally sign it and stuff. https://mathsgear.co.uk/products/humble-pi But it is also available on Amazon. https://www.amazon.co.uk/Humble-Pi-Comedy-Maths-Errors/dp/0241360234/ref=sr_1_1?_encoding=UTF8&tag=stanupmath-21 Thanks to Paul Shepherd from the University of Bath https://researchportal.bath.ac.uk/en/persons/paul-shepherd CORRECTIONS – Nothing yet. Let me…

Infinite Series – Numberphile

From Numberphile. Fields Medallist Charlie Fefferman talks about some classic infinite series. More links & stuff in full description below ↓↓↓ Charles Fefferman at Princeton: https://www.math.princeton.edu/people/charles-fefferman 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…

Overview of differential equations | DE1

From 3Blue1Brown. How do you study what cannot be solved? Home page: https://3blue1brown.com/ Brought to you by you: http://3b1b.co/de1thanks Need to brush up on calculus? https://youtu.be/WUvTyaaNkzM Error correction: At 6:27, the upper equation should have g/L instead of L/g. Steven Strogatz NYT article on the math of love: https://opinionator.blogs.nytimes.com/2009/05/26/guest-column-loves-me-loves-me-not-do-the-math/ Interactive visualization of the example from…

Bayesian Statistics with Hannah Fry

From Standup Mathematician. You can buy Hannah’s great book Hello World from loads of places: http://www.hannahfry.co.uk/helloworld Including signed copies on Maths Gear! https://mathsgear.co.uk/collections/books/products/copy-of-signed-copy-of-hello-world My book Humble Pi is available signed on Maths Gear, as well as un-signed from all the usuals. SIGNED https://mathsgear.co.uk/collections/books/products/humble-pi-a-comedy-of-maths-errors UNSIGNED https://www.amazon.co.uk/Humble-Pi-Comedy-Maths-Errors/dp/0241360234/ref=sr_1_1?_encoding=UTF8&tag=stanupmath-21 The history of Thomas Bayes. http://www-history.mcs.st-andrews.ac.uk/Biographies/Bayes.html All about the theorem…

Live Q + A with Matt Parker

From Standup Mathematician. Thanks for everyone in the live Q+A! Here is the link to buy Humble Pi: https://mathsgear.co.uk/products/humble-pi-a-comedy-of-maths-errors Support me on patreon and I’ll make more videos: https://www.patreon.com/standupmaths Check me out at position number 1! https://www.thetimes.co.uk/magazine/culture/books-the-sunday-times-bestsellers-march-17-g2x7kjsxx Subscribe to my channel and I’ll do more live stuff! Thanks!

What’s special about 277777788888899? – Numberphile

From Numberphile. Matt Parker discusses multiplicative persistence. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) Extra footage: https://youtu.be/E4mrC39sEOQ Matt’s new book is Humble Pi: http://bit.ly/Humble_Pi More Matt videos on Numberphile: http://bit.ly/Matt_Videos The Multiplicative record holders: https://oeis.org/A003001 More info: http://mathworld.wolfram.com/MultiplicativePersistence.html Hear Matt on the Numberphile podcast… http://bit.ly/Numberphile_Pod_Playlist More links & stuff in full…

The Secret of Parabolic Ghosts

From Mathologer. Today we’ll perform some real mathematical magic—we’ll conjure up some real-life ghosts. The main ingredient to this sorcery are some properties of x squared that they don’t teach you in school. Featuring the mysterious whispering dishes, the Mirage hologram maker and some origami x squared.paper magic. Here is a nice article about the…

New Superpermutations Discovered!

From Standup Mathematician. Join in the Superpermutation effort! The superpermutator google group: https://groups.google.com/forum/#!forum/superpermutators Watch the full song in all its 25-minute glory or download it from Bandcamp: https://youtu.be/n4WpyNMfQ2Q https://standupmaths.bandcamp.com/track/5906-superpermutation-by-greg-egan Details about the new superpermutation are on Greg Egan’s website, along with the midi file: http://www.gregegan.net/SCIENCE/Superpermutations/Superpermutations.html#NEWS2 Here is the sheet music if that is your kind…

Pi Day 2019: calculating π with a balancing beam

From Standup Mathematician. http://wwwh.umble-pi.com You can buy my book now! UPDATE: We are out of beam books! Behind the scenes video is here: https://youtu.be/L_pWPM8T-kc Get it from Maths Gear and be guaranteed a signed first edition hard back. https://mathsgear.co.uk/products/humble-pi But it is also available on Amazon. https://www.amazon.co.uk/Humble-Pi-Comedy-Maths-Errors/dp/0241360234/ref=sr_1_1?_encoding=UTF8&tag=stanupmath-21 For teachers (or anyone who would like some…

Humble Pi: Los Angeles crime and Null Island

From Standup Mathematician. http://wwwh.umble-pi.com You can buy my book now! Get it from Maths Gear and be guaranteed a signed first edition hard back. https://mathsgear.co.uk/products/humble-pi But it is also available on Amazon. https://www.amazon.co.uk/Humble-Pi-Comedy-Maths-Errors/dp/0241360234/ref=sr_1_1?_encoding=UTF8&tag=stanupmath-21 The “About the Null island at 0°0’0″ N 0°0’0″ E” post I showed is from the GeoGarage blog: http://blog.geogarage.com/2015/04/about-null-island-at-000-n-000-e.html LAPD crime map…

Humble Pi: plane wrong

From Standup Mathematician. http://wwwh.umble-pi.com Please pre-order my book! It’s out 7 March 2019. Buy it from Maths Gear and be guaranteed a signed first edition hard back. https://mathsgear.co.uk/products/humble-pi But it is also available on Amazon. https://www.amazon.co.uk/Humble-Pi-Comedy-Maths-Errors/dp/0241360234/ref=sr_1_1?_encoding=UTF8&tag=stanupmath-21 More on the Los Angeles Air Route Traffic Control Center mistake: https://www.nytimes.com/2004/09/16/politics/maintenance-lapse-blamed-for-air-traffic-control-problem.html More on the Boeing 787 Dreamliner mistake:…

How fast is a bullet? [featuring: pendulum calculation]

From Standup Mathematician. Thanks to the Cambridge Engineering Department for building the pendulum. http://www.eng.cam.ac.uk/ Much appreciation to Maria Kettle and Cambridge Engineering Outreach for organising the day. http://www.eng.cam.ac.uk/events-and-outreach/schools-and-community-outreach And Hugh was there. http://www2.eng.cam.ac.uk/~hemh1/ The Cambridge University Rifle Association were super helpful and let us take over their range for most of the day! Katherine Fleck…

New Reuleaux Triangle Magic

From Mathologer. Today’s video is about plane shapes that, just like circles, have the same width in all possible directions. That non-circular shapes of constant width exist is very counterintuitive, and so are a lot of the gadgets and visual effects that are “powered” by these shapes: interested in going for a ride on non-circular…

Bad Rounding: ⌊Trump vs Obamacare⌋

From Standup Mathematician. wwwh.umble-pi.com Please pre-order my book! It’s out 7 March 2019. Buy it from Maths Gear and be guaranteed a signed first edition hard back. https://mathsgear.co.uk/products/humble-pi But it is also available on Amazon. https://www.amazon.co.uk/Humble-Pi-Comedy-Maths-Errors/dp/0241360234/ref=sr_1_1?_encoding=UTF8&tag=stanupmath-21 Huffington Post article about 3.49 proposal: http://www.huffingtonpost.com/entry/trump-obamacare-changes_us_5894d9f4e4b040613136d98a?jhf5gjzdv58tcsor “According to sources privy to HHS discussions with insurers, officials would argue…

How colliding blocks act like a beam of light…to compute pi.

From 3Blue1Brown. The third and final part of the block collision sequence. Part 1: https://youtu.be/HEfHFsfGXjs Part 2: https://youtu.be/jsYwFizhncE Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/clacks-thanks Error correction: I wrote the answer as floor(pi/theta), when really it should be ceiling(pi/theta) – 1 t account for values of theta perfectly dividing pi. For example, the…

Superpermutations: the maths problem solved by 4chan

From Standup Mathematician. Join in the Superpermutation effort! The best place to start is the google group: https://groups.google.com/forum/#!forum/superpermutators This is where Robin Houston does his real job: Flourish Data Visualisation http://flourish.studio James Grime’s video: Superpermutations – Numberphile https://www.youtube.com/watch?v=wJGE4aEWc28 A lower bound on the length of the shortest superpattern Anonymous 4chan Poster, Robin Houston, Jay Pantone,…

So why do colliding blocks compute pi?

From 3Blue1Brown. Part 1: https://youtu.be/HEfHFsfGXjs Part 3: https://youtu.be/brU5yLm9DZM Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/clacks-thanks Many of you shared solutions, attempts, and simulations with me this last week. I loved it! Y’all are the best. Here are just two of my favorites. By a channel STEM cell: https://youtu.be/ils7GZqp_iE By Doga Kurkcuoglu: http://bilimneguzellan.net/bouncing-cubes-and-%CF%80-3blue1brown/ And…

The most unexpected answer to a counting puzzle

From 3Blue1Brown. If this doesn’t blow your mind, I don’t know what will. Part 2: https://youtu.be/jsYwFizhncE Part 3: https://youtu.be/brU5yLm9DZM Brought to you by you: http://3b1b.co/clacks-thanks New to this channel? It’s all about teaching math visually. Take a look and see if there’s anything you’d like to learn. NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/…

Irrational Roots

From Mathologer. For the final video for 2018 we return to obsessing about irrational numbers. Everybody knows that root 2 is irrational but how do you figure out whether or not a scary expression involving several nested roots is irrational or not? Meet two very simple yet incredibly powerful tools that they ALMOST told you…

Secrets of the NOTHING GRINDER

From Mathologer. This video is the result of me obsessing about pinning down the ultimate explanation for what is going on with the mysterious nothing grinder aka the do nothing machine aka the trammel of Archimedes. I think what I present in this video is it in this respect, but I let you be the…

But WHY is a sphere’s surface area four times its shadow?

From 3Blue1Brown. The formula is no mere coincidence. Store: http://3b1b.co/store Home page: https://www.3blue1brown.com Special thanks: http://3b1b.co/sphere-thanks Discussion on Reddit: https://www.reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its/ The first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it, and 2/3 the surface area as…

Sneaky Topology | The Borsuk-Ulam theorem and stolen necklaces

From 3Blue1Brown. Solving a discrete math puzzle using topology. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/borsuk-thanks Want more fair division math fun? Check out this Mathologer video https://youtu.be/7s-YM-kcKME (Seriously, Mathologer is great) These videos are supported by the community. https://www.patreon.com/3blue1brown The original 1986 by Alon and West with this proof https://m.tau.ac.il/~nogaa/PDFS/Publications/The%20Borsuk-Ulam%20Theorem%20and%20bisection%20of%20necklaces.pdf VSauce on…