4 ms·
False Mathematics
- lmm 12y agoAn n-dimensional shape can always be cut by n cuts into pieces of strictly smaller diameter. E.g. if you cut a circle in half you get two semicircles of the same diameter as the original circle, but with two cuts you can make three pieces which are all smaller than the original circle. If you cut a sphere with two cuts, you'll always end up with a piece at least as wide as the original sphere (e.g. if you slice it into quarters like an orange, each segment still has the original diameter). It seems intuitively obvious that this is true not just for spheres but for any shape. And indeed it is... up to something like n=7, possibly more. But in e.g. n=2000 the "theorem" is massively, massively false.