3 ms·
Consider an icosahedron. At each vertex a person with a vector pointing outwards. In this example, people are normalized and can be understood by 3 dimensions.
by eipipuz 15y ago
Consider an icosahedron. At each vertex a person with a vector pointing outwards. In this example, people are normalized and can be understood by 3 dimensions. There you have 12 unique persons, each of them an average of the 5 surrounding it. Pick one of them as the best, you will see that doesn't in any way violate that it is still the average.
Anyway, yeah, it also smells bad, but it could have a grain of truth.
- pingswept 15y agoAh, and I had assumed we were scalars! But you're right, and what's even better is that the icosahedron case generalizes to people walking on the surface of a sphere (assuming they're evenly spaced).
- Eliezer 15y agoErm, I could be wrong but wouldn't the icosahedron be the maximum "evenly spaced" set of people on the surface of a sphere (that weren't all confined to a great circle)? Lots of regular polygons, rather fewer regular polyhedra. (Of course if we make the jump to a 4D sphere we can put 600 people into the largest regular polytope, the hexacosichoron. http://en.wikipedia.org/wiki/Convex_regular_4-polytope http://en.wikipedia.org/wiki/Convex_regular_4-polytope) EDIT: I am wrong, it'd only take a uniform polyhedron, not a regular one. E.g. http://en.wikipedia.org/wiki/Icosidodecahedron http://en.wikipedia.org/wiki/Icosidodecahedron