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/ypqcuqcs 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 ways 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)! Some links: John Halton’s proof that the…

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 ↓↓↓ 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 from Ben: https://www.geogebra.org/m/S2W46Thv Catch Ben on the latest Numberphile Podcast: https://youtu.be/-tGni9ObJWk More…

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. 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 Numberphile Podcast: https://youtu.be/-tGni9ObJWk More podcast episodes: http://bit.ly/numberphile_podcast Numberphile is supported by the…

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 —————— The live question setup with stats on-screen is…

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 16:00, the sum should be written with a "…" to indicate going to infinity. At 38:41, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent standard deviation.…

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 —————— 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 on…

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 22:00, I write "b’ / 2" instead of "-b’ /…

Lockdown math announcement

From 3Blue1Brown. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/thanks Innumerable thanks to Ben Eater for helping behind the scenes here: https://www.youtube.com/user/eaterbc —————— Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those…

Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2

From 3Blue1Brown. An introduction to probability density functions Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/thanks Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always great Terence Tao. https://terrytao.files.wordpress.com/2011/01/measure-book1.pdf Also, for the real analysis buffs among you,…

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…

MPMP: Can you play Scrabble over a video call?

From Standup Mathematician. You can enter the submittable part of the puzzle at https://www.think-maths.co.uk/maths-puzzles Everything about Vicki is on her website: https://www.vickipipe.co.uk/ Or go straight to the All The Stations channel! https://www.youtube.com/channel/UC7ttKX46nJxUeXZ0aoD4Q5g Get your own random quantum-noise numbers here: https://qrng.anu.edu.au/ These are my scrabble numbers. I have not double checked them, so please let me…

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 Ben’s website: https://www.bensparks.co.uk Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We…

Why is the Apple Calendar so broken?

From Standup Mathematician. UPDATE: I’m hearing reports of calendar apps crashing quite severely. Please only experiment on non-vital apps as you could hypothetically lose data stored in them! But apparently if the app crashes and restarts don’t fix it: a forced restart will. Proceed with caution, at your own risk, and report any findings! Buy…

Mathematics and Coronavirus – Numberphile

From Numberphile. Featuring Kit Yates… The longer podcast version: https://youtu.be/5OPaDnJ3tm8 Or here: https://www.numberphile.com/podcast/kit-yeates-coronavirus or on your podcast player! More links & stuff in full description below ↓↓↓ Support our videos and podcasts on Patreon: Patreon: http://www.patreon.com/numberphile Kit Yates website – https://kityates.com Kit on Twitter – https://twitter.com/Kit_Yates_Maths The Royal Society’s call to arms for mathematicians –…

Simulating an epidemic

From 3Blue1Brown. Experiments with toy SIR models Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/sir-thanks Awesome fan-made interactives: https://prajwalsouza.github.io/Experiments/Epidemic-Simulation.html https://learningsim.itch.io/pandemic-spread-simulation Simulations by Harry Stevens at the Washington Post: https://www.washingtonpost.com/graphics/2020/world/corona-simulator/ Simulations by Kevin Simler at Melting Asphalt: https://meltingasphalt.com/interactive/outbreak/ Excellent visualization of each country’s current growth from Minutephysics and Aatish Bhatia: https://www.youtube.com/watch?v=54XLXg4fYsc Another good interactive to…

The Coronavirus Curve – Numberphile

From Numberphile. Ben Sparks explains (and codes) the so-called SIR Model being used to predict the spread of cornavirus (COVID-19). More links & stuff in full description below ↓↓↓ National Health Service (UK) advice on Coronavirus: https://www.nhs.uk/conditions/coronavirus-covid-19/ Ben Sparks: https://www.bensparks.co.uk Use the Geogebra file Ben created for this video: https://www.geogebra.org/m/nbjfjtpv Another good file courtesy of…

Why do people keep getting this wrong‽

From Standup Mathematician. UK tour show details will be updated here: http://standupmaths.com/shows/ Check out Christian Lawson-Perfect’s cash calculator: https://make-it-rain-bloomberg.glitch.me/ https://twitter.com/christianp/status/1236338871564226561 US edition of Humble Pi http://bit.ly/humblepi UK edition of Humble Pi https://www.penguin.co.uk/books/300/300640/humble-pi/9780141989143.html Sorry, Think Maths have not made any teacher resources for this video, but check out their resources for all my other videos here:…

Binomial distributions | Probabilities of probabilities, part 1

From 3Blue1Brown. Part 2: https://youtu.be/ZA4JkHKZM50 Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/beta1-thanks John Cook post: https://www.johndcook.com/blog/2011/09/27/bayesian-amazon/ —————— These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it’s not the most well-documented tool, and it has…

Mesolabe Compass and Square Roots – Numberphile

From Numberphile. Johnny Ball on the "often missed" Hippocrates of Chios. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More on Johnny Ball, including his books and live shows: https://www.johnnyball.co.uk See Johnny discuss Russian multiplication: https://youtu.be/HJ_PP5rqLg0 Numberphile is supported by the Mathematical Sciences…

Random Fibonacci Numbers – Numberphile

From Numberphile. Dr James Grime on random Fibonacci Sequences… Extra footage: https://youtu.be/F0C4U7Q5yXU More links & stuff in full description below ↓↓↓ Fibonacci Numbers in the Mandelbrot Set: https://youtu.be/4LQvjSf6SSw More James Grime videos: http://bit.ly/grimevideos Our podcast interview with James Grime: https://youtu.be/9gQzkKifd3U or https://apple.co/2HsUMKb James Grime website: https://www.singingbanana.com Numberphile is supported by the Mathematical Sciences Research Institute…

Will a falling pencil hit the table? We do the maths!

From Standup Mathematician. Do check out Jane Street’s Real Numbers: https://www.janestreet.com/real-numbers Here is a scan of all the working out: https://www.dropbox.com/s/e0gg5bc891kny3t/pencil-maths.pdf?dl=0 We have a full break down of the working out for teachers: http://think-maths.co.uk/standupmaths-videos?yt-pencils#pencils There are Think Maths free resources for teachers for most of my videos! http://think-maths.co.uk/standupmaths-videos CAMERA ISSUE Yes we did lose the…

Why was this visual proof missed for 400 years? (Fermat’s two square theorem)

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer and get your name in the credits of Mathologer videos Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today’s video is about a new really wonderfully simple and visual proof of Fermat’s famous two square theorem: An odd prime can be…

The Datasaurus Dozen

From Standup Mathematician. Pre-order Humble Pi in the USA here: http://bit.ly/humblepi Watch Adam Savage announce his first book club! https://www.youtube.com/watch?v=yr0M5a1eTW0 Huge thanks to Justin Matejka for taking the time to chat with me. They do some amazing work. Follow Justin on twitter! https://twitter.com/JustinMatejka Read all about Justin’s plot and the Datasaurus Dozen here: https://www.autodeskresearch.com/publications/samestats Check…