POW #1: Two Closed Curves

With a black pen draw a closed curve of any shape you please. Then with a red pen draw a second curve over the first one, the only restriction being that you can never pass through a previously created intersection. (Note: all crossings must be "transverse", that is, one curve can't tangentially intersect another.) Circle all points where one curve crosses the other. Prove that the number of such points must be even.


Return to Laura Taalman, Burruss 127, by 2/4/04.