That sounds fascinating. Why are they pointy?
re: long, higher-dimensional geometry
@dodec separately (but probably relatedly in some way we can't be bothered to figure out), the "volume" of a higher-dimensional sphere shrinks extremely fast--it grows as πⁿ/n! (where n is half the dimension), and the factorial wins out here, as factorials tend to do
so you have a shape that reaches out really far while having a really small volume
-F
re: long, higher-dimensional geometry
@dodec Round is spiky in 100-dimensional space!
-F
re: long, higher-dimensional geometry
@Felthry
Yeah, that makes sense. And, of course, they're still round. Higher-dimensional geometry is extremely weird.