For a little animation of Conway's(?) extreme proof, gosper.org/homeplate.html --rwg -------- Original Message -------- Date: 2017-08-14 12:37 From: Thane Plambeck <tplambeck@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Cc: "Schroeppel, Richard" <rschroe@sandia.gov> Reply-To: math-fun <math-fun@mailman.xmission.com> suppose P is a convex polygon with vertices at the usual integer (2d) lattice points (Z2) Is P necessarily similar to a polygon T obtained by (1) deleting finitely many points from Z2, and then (2) computing the Voronoi cells of the remaining points? if the answer is yes, then up to similarity, every convex polygon with Z2 vertices has (up to similarity) a Voronoi deletion birthday. for example, the square has birthday zero. a "picket" shaped polygon of area 1.25 is the unique polygon at birthday one. three more are born at day two, including a pentagon that is obviously the "correct" resolution of the Major League Baseball impossible home plate problem, described here http://mathworld.wolfram.com/HomePlate.html another example: what is the birthday of the 45-45-90 triangle? i worked with a high school student, Michael Nizsenson, on related problems recently. [megachop]