How to partition a quadrilateral into a finite number of equal-area triangles - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T03:17:00Z http://mathoverflow.net/feeds/question/105067 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105067/how-to-partition-a-quadrilateral-into-a-finite-number-of-equal-area-triangles How to partition a quadrilateral into a finite number of equal-area triangles bo.gu 2012-08-20T02:31:05Z 2012-08-20T03:51:25Z <ol> <li><p>A quadrilateral can be partitioned into 2 equal-area triangles if and only if one diagonal divides equally the other diagonal.</p></li> <li><p>It can be proved that most quadrilaterals cannot be partitioned into 3 equal-area triangles.</p></li> <li><p>Conjecture: For any natural number \$n\$, there exists a quadrilateral that cannot be partitioned into \$n\$ equal-area triangles.</p> <p>How can one prove this?</p></li> </ol> <p>[Original question by <a href="http://mathoverflow.net/users/20491/bo-gu" rel="nofollow">bo.gu</a> (MO user20491).]</p> http://mathoverflow.net/questions/105067/how-to-partition-a-quadrilateral-into-a-finite-number-of-equal-area-triangles/105069#105069 Answer by Igor Rivin for How to partition a quadrilateral into a finite number of equal-area triangles Igor Rivin 2012-08-20T02:37:40Z 2012-08-20T02:37:40Z <p>See <a href="http://en.wikipedia.org/wiki/Equidissection" rel="nofollow">this Wikipedia article.</a></p>