Simple yet 5000 years missed ?

From Mathologer. Good news! You really can still discover new beautiful maths without being a PhD mathematician. Stumbled across this one while working on the magic squares video. Another curious discovery by recreational mathematician Lee Sallows. A simple and beautiful and curious fact about triangles that, it appears, was first discovered only 10 years ago.…

What’s the curse of the Schwarz lantern?

From Mathologer. Second coop with Andrew. This time it’s about the Schwarz lantern a very famous counterexample to something that mathematicians believed to be obviously true. A 3D cousin of the famous pi = 4 paradox. 00:00 Intro 00:39 Troll math: the pi=4 meme 02:25 Archimedes chops off corners 05:51 Archimedes boxing of pi 07:40…

The best A – A ≠ 0 paradox

From Mathologer. This video is about a new stunning visual resolution of a very pretty and important paradox that I stumbled across while I was preparing the last video on logarithms. 00:00 Intro 00:56 Paradox 03:52 Visual sum = ln(2) 07:58 Pi 11:00 Gelfond’s number 14:22 Pi exactly 17:35 Riemann’s rearrangement theorem 22:40 Thanks! Riemann…

Powell’s Pi Paradox: the genius 14th century Indian solution

From Mathologer. Around 1400 there lived an Indian astronomer and mathematician by the name of Madhava of Saṅgamagrāma. He was the greatest mathematician of his time and, among other mathematical feats, he and his followers managed to discover a lot of calculus 200 years before Newton and Leibniz did their thing. While preparing a video…

Fibonacci = Pythagoras: Help save a beautiful discovery from oblivion

From Mathologer. In 2007 a simple beautiful connection Pythagorean triples and the Fibonacci sequence was discovered. This video is about popularising this connection which previously went largely unnoticed. 00:00 Intro 07:07 Pythagorean triple tree 13:44 Pythagoras’s other tree 16:02 Feuerbach miracle 24:28 Life lesson 26:10 The families of Plato, Fermat and Pythagoras 30:45 Euclid’s Elements…

Secrets of the lost number walls

From Mathologer. This video is about number walls a very beautiful corner of mathematics that hardly anybody seems to be aware of. Time for a thorough Mathologerization 🙂 Overall a very natural follow-on to the very popular video on difference tables from a couple of months ago ("Why don’t they teach Newton’s calculus of ‘What…

Why is calculus so … EASY ?

From Mathologer. Calculus made easy, the Mathologer way 🙂 00:00 Intro 00:49 Calculus made easy. Silvanus P. Thompson comes alive 03:12 Part 1: Car calculus 12:05 Part 2: Differential calculus, elementary functions 19:08 Part 3: Integral calculus 27:21 Part 4: Leibniz magic notation 30:02 Animations: product rule 31:43 quotient rule 32:18 powers of x 33:10…

Heron’s formula: What is the hidden meaning of 1 + 2 + 3 = 1 x 2 x 3 ?

From Mathologer. Today’s video is about Heron’s famous formula and Brahmagupta’s and Bretschneider’s extensions of this formula and what these formulas have to do with that curious identity 1+2+3=1x2x3. 00:00 Intro 01:01 1+2+3=1x2x3 in action 02:11 Equilateral triangle 02:30 Golden triangle 03:09 Chapter 1: Heron 06:18 Heron’s formula 08:50 Brahmagupta’s formula 10:20 Bretschneider’s formula 11:52…

Reinventing the magic log wheel: How was this missed for 400 years?

From Mathologer. Today is about reinventing a really cool mathematical wheel and its many different slide rule incarnations, just using a rubber band. 00:00 Intro 04:40 Multiply! 06:02 Pi times e 07:15 Divide! 08:39 Sliding rules 10:53 Apollo 11:08 Star Trek 11:45 Rubber band proof 13:13 Logarithms 16:50 Dmitry’s wheel 17:48 Thank you! This video…