The mathematical soul of juggling @Mathologer

Uploaded December 2015 | Updated September 2026, 2 weeks ago

In this video the Mathologer captures the mathematical soul of juggling and has a lot of fun analysing the hell out of it.

If you are really keen check out his book and articles on the math of juggling:
tinyurl.com/glczdxl
tinyurl.com/pryz6fw
qedcat.com/books.html

The animations at the end of this video were created a while ago with the free juggling animators Juggle Master and JoePass! These programs are a bit outdated. If you want to play with some animators maybe also check out Jongl and Juggling Lab. Juggling Lab also includes some very nice analytic tools.

Oh, and just in general, if you'd like to google around for more try "site swap juggling" and check out my juggling intro here youtu.be/xaaQs5w1X0s

Enjoy!

PETRS MIRACLE: Why was it lost for 100 years? (Mathologer Masterclass)

$Eulers infinite pi formula generator Today we derive them all, the most famous infinite pi formulas: The Leibniz-Madhava formula for pi, John Walliss infinite product formula, Lord Brounckers infinite fraction formula, Eulers Basel formula and its infinitely many cousins. And we do this starting with one of Eulers crazy strokes of genius, his infinite product formula for the sine function. This video was inspired by Paul Levries one-page article Eulers wonderful insight which appeared in the Mathematical Intelligencer in 2012. Stop the video at the right spot and zoom in and have a close look at this article or download it from here https://link.springer.com/journal/283/34/4 Very pretty. If you are a regular and some of what I talk about in this video looks familiar thats not surprising since weve visited this territory before in Eulers real identity NOT e to the i pi = -1: https://youtu.be/yPl64xi_ZZA 0:00 Intro 1:49 A sine of madness. Eulers ingenious derivation of the product formula for sin x 7:43 Wallis product formula for pi: pi/2 = 2*2*4*4*6*6*.../1*3*3*5*5*... 9:16 Leibniz-Madhava formula for pi: pi/4=1-1/3+1/5-1/7+... 11:50 Brounckers infinite fraction formula for pi: 4/pi = ... 18:31 Eulers solution to the Basel problem: pi^2/6=1/1^2+1/2^2+1/3^2+... 21:51 More Basel formulas for pi involving pi^4/90=1/1^4+1/2^4+1/3^4+... , etc. Music (all from the free audio library that YouTube provides to creators): https://www.youtube.com/audiolibrary/music?nv=1 Take me to the Depth (chapter transitions) Fresh fallen snow Morning mandolin English country garden Enjoy! Burkard$ $The PROOF: e and pi are transcendental Today’s video is dedicated to introducing you to two of the holy grails of mathematics, proofs that e and pi are transcendental numbers. For the longest time I was convinced that these proofs were simply out of reach of a self-contained episode of Mathologer, and I even said so in a video on transcendental numbers last year. Well, I am not teaching any classes at uni this semester and therefore got a bit more time to spend on YouTube. And so I thought why not sink some serious time into trying to make this “impossible” video anyway. I hope you enjoy the outcome and please let me know in the comments which of the seven levels of enlightenment that make up this video you manage to conquer. Even if you just make it to the end of level one it will be an achievement and definitely worth it :) 0:00 Intro 1:48 Enter Transcendence 2:12 Level 1 - e - irrational 6:40 Level 2 - e - quadratic irrational 10:03 Level 3 - e - master proof 12:47 Level 4 - e - gamma 26:14 Level 5 - pi - Lindemann’s trick 29:59 Level 6 - pi - transcendence 35:35 Level 7 Today’s video would have been impossible without the help from my analyst colleague and friend Marty Ross who did most of the heavy lifting in terms of identifying and adapting the least crazy transcendence proofs for e and pi in existence for this video. Here is Marty’s writeup of the infinite series based proof that e is not a quadratic irrational http://www.qedcat.com/notes/e%20not%20quadratic.pdf and here is his formal write-ups of the proofs for the transcendence of pi and e that this video is based on http://www.qedcat.com/notes/e%20+%20pi%20transcendental.pdf. Marty’s version of the proofs is based on this paper by Steinberg and Redheffer https://projecteuclid.org/download/pdf_1/euclid.pjm/1103051870 which in turn has its origins in a proof by David Hilbert http://www.cs.toronto.edu/~yuvalf/Hilbert%20Ueber%20die%20Transzendenz%20der%20Zahlen%20e%20und%20pi.pdf. Apart from Marty I’d also like to thank MIchael Fraklin for his help with recording this episode of Mathologer, as well as Danil Diitriev who as usual will take care of the preparing amazing Russian subtitles for this video. The mysterious Buddhabrot fractal was discovered by Melinda Green. For an intro to this strange mathematical creature check out my Mandelbrot video. http://youtu.be/9gk_8mQuerg Finally, here is a playlist of all my videos on irrational and transcendent numbers. http://www.youtube.com/playlist?list=PLmNp3NTX4KXK6-xgFJdMAbavzgQaKjRzY Enjoy :) Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details)$

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The mathematical soul of juggling