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…

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 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…

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. 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…

Fermat’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…

Toroflux paradox: making things (dis)appear with math

From Mathologer. Today is all about geometric appearing and vanishing paradoxes and that math that powers them. This video was inspired by a new paradox of this type that Bill Russel from Bakersfield, California discovered while playing with a toroflux. Other highlights to look forward to: a nice new visual proof of Cassini’s Fibonacci identity…

The PROOF: e and pi are transcendental

From Mathologer. 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…

The fix-the-wobbly-table theorem

From Mathologer. This video is about the absolutely wonderful wobbly table theorem. A special case of this theorem became well-known in 2014 when Numberphile dedicated a video to it: A wobbling square table can often be fixed by turning it on the spot. Today I’ll show you why and to what extent this trick works,…

Epicycles, complex Fourier series and Homer Simpson’s orbit

From Mathologer. Today’s video was motivated by an amazing animation of a picture of Homer Simpson being drawn using epicycles. This video is about making sense of the mathematics epicycles. Highlights include the surprising shape of the Moon’s orbit around the Sun, instructions on how you can make your own epicycle drawings, and a crash…

What’s the Monkey number of the Rubik’s cube?

From Mathologer. The “Monkey number” is the average number of twists it takes to solve a Rubik’s cube starting from a randomly chosen scrambled position and by making random twists. It’s pretty obvious that this number will be gigantic but nobody knows the exact value of this number nor even how gigantic a number we…

The golden ratio spiral: visual infinite descent

From Mathologer. So you all know the golden (ratio) spiral. But did you know that not only the golden ratio but really every number has such a spiral associated with it? And that this spiral provides key insights into the nature of a number. Featuring more proofs by contradiction by infinite descent (my current obsession),…

Visualising irrationality with triangular squares

From Mathologer. Get ready for some brand new and very pretty visual proofs of the fact that root 2, root 3, root 5 and root 6 are irrational numbers. Root 2 being irrational also translates into the fact that the equation x^2+x^2=y^2 has no solutions in positive integers, root 3 being irrational translates into the…

Euler’s and Fermat’s last theorems, the Simpsons and CDC6600

From Mathologer. This video is about Fermat’s last theorem and Euler’s conjecture, a vast but not very well-known generalisation of this super theorem. Featuring guest appearances by Homer Simpson and the legendary supercomputer CDC6600. The video splits into a fairly easygoing first part and a hardcore second part which is dedicated to presenting my take…