A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square. The post The Biggest Smallest Triangle Just Got Smaller first appeared on Quanta Magazine
Consider a square with a bunch of points inside. Take three of those points, and you can make a triangle. Four points define four different triangles. Ten points define 120 triangles. The numbers grow quickly from there — 100 points define 161,700 different triangles. Each of those triangles, of course, has a particular area. Hans Heilbronn, a German mathematician who fled his country before World…