Tiling the unit square with 5 rational triangles

摘要

There are 14 distinct ways to tile the unit square (modulo the symmetries of the square) with 5 triangles such that the 5-tiling is not a subdivision of a tiling using fewer triangles. We demonstrate how to construct infinitely many rational tilings in each of the 14 configurations. This stands in contrast to a long standing inability to find rational 4-tilings of the unit square in the so-called X-configuration.