Curves on a Sphere
Here’s a riddle from Peter Winkler‘s book “Mathematical Mind-Benders” (which is wholeheartedly recommended):
On the surface of a sphere of radius 1 lies a closed curve of length less then . Prove that it is contained in some hemisphere.
Since there are currently no readers to this probablog, there’s no reason to wait a couple of days before posting hints or solutions, beside procrastination. Well, I guess that’s a good enough reason for me.
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