# Fermat’s Christmas theorem: Visualising the hidden circle in pi/4 = 1-1/3+1/5-1/7+…

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Leibniz’s formula pi/4 = 1-1/3+1/5-1/7+… is one of the most iconic pi formulas. It is also one of the most surprising when you first encounter it. Why? Well, usually when we see pi…

# Secret of row 10: a new visual key to ancient Pascalian puzzles

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today’s video is about a recent chance discovery (2002) that provides a new beautiful visual key to some hidden self-similar patterns in Pascal’s triangle and some naturally occurring patterns on snail shells. Featuring,…

# Power sum MASTER CLASS: How to sum quadrillions of powers … by hand! (Euler-Maclaurin formula)

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) The longest Mathologer video ever! 50 minutes, will this work? Let’s see before I get really serious about that Kurosawa length Galois theory video ðŸ™‚ Today’s video is another self-contained story of mathematical…

# 500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can’t handle?

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Why is it that, unlike with the quadratic formula, nobody teaches the cubic formula? After all, they do lots of polynomial torturing in schools and the discovery of the cubic formula is considered…

# 2000 years unsolved: Why is doubling cubes and squaring circles impossible?

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today’s video is about the resolution of four problems that remained open for over 2000 years from when they were first puzzled over in ancient Greece: Is it possible, just using an ideal…

# Solving EQUATIONS by tagging TURTLES with LASERS

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) 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…

# The Secret of Parabolic Ghosts

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) 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…

# New Reuleaux Triangle Magic

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) 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…

# The secret of the 7th row – visually explained

From Mathologer. In 1995 I published an article in the Mathematical Intelligencer. This article was about giving the ultimate visual explanations for a number of stunning circle stacking phenomena. In today’s video I’ve animated some of these explanations. Here is a copy of a preprint of the Intelligencer article: http://www.qedcat.com/misc/stacks.pdf And here are links to…

# Irrational Roots

From Mathologer. iNEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) 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…

# Secrets of the NOTHING GRINDER

From Mathologer. NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) 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…

# Fermatâ€™s HUGE little theorem, pseudoprimes and Futurama

From Mathologer. A LOT of people have heard about Andrew Wiles solving Fermat’s last theorem after people trying in vain for over 350 years. Today’s video is about Fermat’s LITTLE theorem which is at least as pretty as its much more famous bigger brother, which has a super pretty accessible proof and which is of…