4 ms·
The spheres and the cubes are of the same dimension, so it's not like trying to put flat things inside of a thing with volume. (Technically I should have said m
by Strilanc 8y ago
The spheres and the cubes are of the same dimension, so it's not like trying to put flat things inside of a thing with volume. (Technically I should have said million dimensional balls instead of spheres. Sorry if that was confusing.)
- sudhirj 8y agoThen isn’t the answer 1? For 2 dimensions, one circle fits in a square, in three dimensions one sphere fits in a cube. Should be the same for any value of n?
- Strilanc 8y agoConsider that the distance between opposite corners of a square is √2 meters, but for a cube it's √3 meters. In general, for an n-dimensional hypercube of diameter 1m, the exactly-opposite corners are √n meters apart. Meaning, in a million-dimensional meter-diameter hypercube, exactly-opposite corners will be a kilometer apart. There's a lot more diagonal wiggle room than you think.
- therein 8y agoThat blew my mind but it still sounds like it would generalize, wouldn't it?