Hoggatt and Denman showed that any obtuse triangle can be divided into eight acute isosceles triangles. There are 1, 4, 23, 180, 1806, 20198, ... (OEIS A056814) topologically distinct ways to divide a triangle into n = 2, 3, ... smaller triangles (Vicher). A triangle partition is prime if it does not contain a triangle partition of lower order. The number of prime triangle partitions of orders n = 2, 3, ... are 1, 1, 3, 8, 62, 535, 4213, ... (OEIS A053740).

integer triangle | square dissection | triangle dissection paradox