any subset of points. For these subsets form simplices but for larger values relative they can form more complicated shapes. When is sufficiently large relative randomly placed point sets have minimum convex hull No better bound is possible; any placement has points with obtained by choosing some consecutive points in coordinate order. This result has applications in range searching data structures. See also Danzer set, a set of points that avoids empty triangles of large area Notes References External links Erich's Packing Center, by Erich Friedman, including the best known solutions to the Heilbronn problem for small values of for squares, circles, equilateral triangles, and convex regions of variable shape but fixed area Discrete geometry Triangle problems Area Discrepancy theory