Fair Dice (Part 1) - Numberphile
Probability expert Professor Persi Diaconis (Stanford University) talking about dice. More links & stuff in full description below ↓↓↓ Part 2: ...
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So a cube has perfect symmetry, right? You know what I mean. Every face is the same. And a tetrahedron has perfect symmetry. Okay, there are four faces, and they're all the same. You can ask, and Euclid did, what are all of the symmetric three-dimensional objects? And it turns out there are only five of them. Most people know what a cube is, and a tetrahedron. But there are also an octahedron, which has eight faces, you know, four on top and four on the bottom. And it's again, perfectly symmetrical. Every way you twist and turn it, it looks the same, just like a cube. And then there are two others. There's the icosahedron and the dodecahedron. But that's it. So first you might think, well, if there are so many funny ones, why aren't there lots of different ones? So I proved tha...
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So a cube has perfect symmetry, right? You know what I mean. Every face is the same. And a tetrahedron has perfect symmetry. Okay, there are four faces, and they're all the same. You can ask, and Euclid did, what are all of the symmetric three-dimensional objects? And it turns out there are only five of them. Most people know what a cube is, and a tetrahedron. But there are also an octahedron, which has eight faces, you know, four on top and four on the bottom. And it's again, perfectly symmetrical. Every way you twist and turn it, it looks the same, just like a cube. And then there are two others. There's the icosahedron and the dodecahedron. But that's it. So first you might think, well, if there are so many funny ones, why aren't there lots of different ones? So I proved tha...
