A german dude with an amazing head for maths.
From Mathologer. Today’s mission is to reveal a surprisingly simple trick that lets you use any old ax(e) to calculate the area of plane shapes. More broadly, we’ll explore planimeters — mechanical instruments that compute area by tracing a shape’s edge. Real mathematical magic in action! 00:00 Intro (a mathematical fairy tale) 07:16 Cool machines…
From Mathologer. Today we are solving an ancient bankruptcy puzzle from the Talmud using the principle of communicating vessels. A very nice visual way of making sense of an otherwise tricky problem. "Game theoretic analysis of a bankruptcy problem from the Talmud" by Robert J Aumann and Michael Maschler https://www.sciencedirect.com/science/article/pii/0022053185901024 " ‘Hydraulic’ rationing" by Marek…
From Mathologer. This is a corrected version of a video that I uploaded two days ago. After a critical mistake was discovered in the "Nature’s Numbers" part of the video, I decided to scrap the original video, fix the errors and republish the video (many more hours down the drain 🙁 Anyway, had to be…
From Mathologer. The third video in a trilogy of Mathologer videos dealing with sum-equals-product identities and equations. The other two are: Way beyond the golden ratio The power of AB=A+B (Mathologer masterclass) Heron’s formula: What is the hidden meaning of 1 + 2 + 3 = 1 x 2 x 3 ? Today’s video is…
From Mathologer. We are making history again by presenting a new visual proof of the 2000+ years old Ptolemy’s theorem and Ptolemy’s inequality. 00:00 Introduction 04:27 Geometry 101 08:19 Applications 14:46 Ptolemy’s inequality 18:34 LIES 25:35 Animated proofs 28:57 Thank you! 30:53 Degenerate Easter Egg There are some other proofs of Ptolemy’s theorem/inequality based on…
From Mathologer. Today’s mission: saving another incredible discovery from falling into oblivion: Steinbach’s amazing infinite family of counterparts of the golden ratio discovered around 1995. Lot’s of my own little discoveries in this one 🙂 00:00 Intro 05:53 Ptolemy 09:18 Perfect cut 16:01 Golden rectangle 22:03 Fibonacci 33:07 A+B=AB 45:48 Images and music 47:27 Thank…
From Mathologer. Today’s topic is the Petr-Douglas-Neumann theorem. John Harnad told me about this amazing result a couple of weeks ago and I pretty much decided on the spot that this would be the next Mathologer video. I really had a lot of fun bringing this one to life, maybe too much fun 🙂 Very…
From Mathologer. Conway’s whatever … it’s named after John Conway and so it must be good 🙂 Wiki page dedicated to John Conway https://en.wikipedia.org/wiki/John_Horton_Conway Wiki page Conway’s circle https://en.wikipedia.org/wiki/Conway_circle_theorem Wiki page on his Game of Life https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life Michael de Villiers (the connection with the windscreen wiper theorem, read this one first) http://dynamicmathematicslearning.com/conway-circle-theorem-special-case-side-divider-theorem.pdf http://dynamicmathematicslearning.com/conway-circle-as-special-side-divider-theorem.html Also check…
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.…
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…
From Mathologer. In today’s video we’ll make a little bit of mathematical history. I’ll tell you about a major upgrade of one of Archimedes’ greatest discoveries about the good old sphere that so far only a handful of mathematicians know about. 00:00 Intro to the baggage carousel 01:04 Archimedes baggage carousel 04:26 Inside-out animations 04:59…
From Mathologer. The painter’s paradox, a.k.a. Gabriel’s horn paradox a.k.a. Torricelli’s horn paradox has been done to death on YouTube. So why do it again? Well, being all about some remarkable features of 1/x, this topic nicely complements the previous two videos that were also dedicated to 1/x. Now the first Mathologer trilogy is complete!…
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…
From Mathologer. Simple visual logarithms. Is there such a thing? You bet 🙂 00:00 Intro 01:59 Rubik’s cube and drill 03:26 What’s the area? 05:15 Sum of 1+1/2+1/3+… 06:35 Mystery sum 11:32 What base? 17:25 What is Log_b(x)? 22:14 Is this a circle? 28:53 Proof that e^a = cosh(a) + sinh(a) 30:50 Thanks Maths of…
From Mathologer. In this masterclass video we’ll dive into the mind of the mathematical genius Srinivasa Ramanujan. The focus will be on rediscovering one of his most beautiful identities. 00:00 Intro 02:48 How did his mind work? 09:12 What IS this? 15:11 Fantastic fraction 18:12 Impossible identity 23:38 Thanks! This video was inspired by two…