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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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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Every Proof of the Pythagorean Theorem Explained

https://www.youtube.com/watch?v=sfkzxznVtcQ The Pythagorean theorem is one of the oldest and most famous results in mathematics. More than 370 proofs of the theorem are known,…

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Math Has Exactly 5 Perfect Shapes

https://www.youtube.com/watch?v=mqodRLuPCtw Take a three-dimensional shape in which every face is the same regular polygon, such as an equilateral triangle, square, or regular pentagon, and…

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Every Unsolved Geometry Problem that Sounds Easy – Part 2

Five More Geometry Problems That Are Way Harder Than They Look Tripod PackingThe Thomson ProblemThe Levi-Hadwiger ConjectureHeesch’s ProblemKalai’s 3ᵈ Conjecture Tripod Packing Let’s start…

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Every Complex Geometry Shape Explained 2

The Apollonian Gasket The Golden Spiral The Three-Torus The Mucube The Burning Ship Fractal The Apollonian Gasket Let’s start by drawing a circle named…

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Every Angle Unit Explained in 10 minutes

The Turn The Degree The Radian The Gradian Binary Angular Measurement The Turn An angle is formed between two rays that share an endpoint….

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