Simon came up with what he calls a conjecture about the minimum number of equilateral triangles that fit into a larger equilateral triangle. He has discovered that for equilateral triangles that have a length of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 the minimum number of equilateral triangles that fit into them is consecutively 4, 6, 4, 8, 4, 10, 4, 6, 4, 12, 4, i.e. a sequence with a repetitive pattern. In the two videos about Simon’s Triangles Conjecture, Simon explains this discovery and presents his proof. He supposes that the pattern continues for even larger triangles, but has proven it up to the side length of 12 so far.