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 2 \pi. 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.


~ by Ori on October 16, 2008.

2 Responses to “Curves on a Sphere”

  1. […] Following my own riddle post (OK, not really), Gil Kalai posted two math riddles. I would like to offer a variation on the ant […]

  2. […] on a Sphere – the Solution Here’s the riddle and a solution. And here’s a solution fitting a […]

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: