Given a partition of a square into n triangles of equal area, prove that n is even.

(In reply to re(3): Part I - notation by Richard)

This really is not an elementary problem, Richard.

Paul Monsky's solution¹, in his own words, "is the only known approach, and it uses valuation theory, and the theorem of the extension of valuations--a mathematician will probably encounter these for the first time as a graduate student."

¹American Mathematical Monthly 77:2(February 1970, 161-164)

Posted by Mindrod on 2006-02-04 20:14:26