

False Mathematics - todd8
http://math.stackexchange.com/questions/820686/obvious-theorems-that-are-actually-false

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lmm
An _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.

