The re-launching of this question is quite timely, as experimental math was behind a beautiful recent discovery of a new way to tile the plane with a pentagon. Previously only 14 such tilings were known. The new and 15th tiling announced a few weeks ago was discovered by Casey Mann, Jennifer McLoud and David Von Derau using a computer search:
http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/aug/10/attack-on-the-pentagon-results-in-discovery-of-new-mathematical-tilehttps://www.theguardian.com/science/alexs-adventures-in-numberland/2015/aug/10/attack-on-the-pentagon-results-in-discovery-of-new-mathematical-tile
