The Pigeon Hole Principle: 7 gorgeous proofs 0 (0)

From Mathologer. Let’s say there are more pigeons than pigeon holes. Then, if all the pigeons are in the holes, at least one of the holes must house at least two of the pigeons. Completely obvious. However, this unassuming pigeon hole principle strikes all over mathematics and yields some really surprising, deep and beautiful results.…

The ultimate algorithm 0 (0)

From Mathologer. There must be millions of people who have heard of the Tower of Hanoi puzzle and the simple algorithm that generates the simplest solution. But what happens when you are playing the game not with three pegs, as in the original puzzle, but with 4, 5, 6 etc. pegs? Hardly anybody seems to…

How did Ramanujan solve the STRAND puzzle? 0 (0)

From Mathologer. Today’s video is about making sense of an infinite fraction that pops up in an anecdote about the Indian mathematical genius Srinivasa Ramanujan. 00:00 Intro 04:31 Chapter 1: Getting a feel for the puzzle 08:27 Chapter 2: Algebra autopilot 12:37 Chapter 3: Infinite fraction 17:51 Chapter 4: Root 2 21:19 Chapter 5: Euclidean…

Euler’s crazy pi formula generator 0 (0)

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…

Fermat’s Christmas theorem: Visualising the hidden circle in pi/4 = 1-1/3+1/5-1/7+… 0 (0)

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 0 (0)

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) 0 (0)

From Mathologer. 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 🙂 Today’s video is another self-contained story of mathematical discovery covering millennia of math, starting from pretty much nothing and finishing with a mathematical mega weapon that usually only…

The Secret of Parabolic Ghosts 0 (0)

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…