Why You Can’t Draw These 4 Shapes Exactly

https://www.youtube.com/watch?v=HycahwKr0CA With only an unmarked straightedge and a compass, ancient geometers could bisect angles, build equilateral triangles and draw regular pentagons. Yet four simple-sounding…

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Every Perfect 4D Shape Explained

https://www.youtube.com/watch?v=fqJBWqUpA3I The tesseract is the best-known four-dimensional shape, yet it is only one of six perfectly regular convex shapes in four dimensions. Each is…

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We Know Everything About This Number Except Whether It Exists

https://www.youtube.com/watch?v=Nlp-qSP5y3o Some numbers are defined so precisely that we know almost everything about them, except whether a single example exists. This article explores quasiperfect…

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Every Knot From Simplest to Impossible Explained

https://www.youtube.com/watch?v=Nyn3dLjqicA Take a loop of rope, tie a knot, glue the ends together, and hold it to a mirror: for some knots, the reflection…

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Every Shape That Can Roll Without Being Round Explained

https://www.youtube.com/watch?v=sXxMhf1mqAs A wheel does not have to be a circle. Some strange shapes can roll smoothly between two parallel surfaces, and others can roll…

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Every Weird Shape That Shouldn’t Exist Explained

https://www.youtube.com/watch?v=q198_ySulTc Some mathematical objects seem to break the rules of geometry. A curve that has area, a sponge with no volume but endless surface,…

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The Most Controversial Proof in Mathematics Ever

https://www.youtube.com/watch?v=s-J0TWF93WM Mathematics rests on a promise: if a proof is correct, a trained mathematician should be able to check it. Shinichi Mochizuki's claimed proof…

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Every Particle in Physics Explained

https://www.youtube.com/watch?v=rq1VxNTiP1A   Every Fundamental Particle in the Standard Model Explained What is everything made of? The Standard Model of particle physics describes the smallest…

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Every Weird Number That Shouldn't Exist Explained

https://www.youtube.com/watch?v=RP3vR-6egrs Thanks for watching! Chapters: 0:00 Zero 1:40 Negative Numbers 2:40 Imaginary Numbers 3:39 Infinitesimals 4:44 Surreal Numbers 5:55 Quaternions 7:00 Octonions 8:32 Transfinite…

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