Special Collection: Triangles in a square
There are 10 entries in this table of similar, but not identical, triangles tiling a square.
The two properties are the number of triangles and the smallest angle of the triangles, which
are all right-angled triangles.
A paper giving the method devised by Tony Lee appears here.
NB. The colours are chosen at random.
It is known that a square can the tiled with similar triangles which do not have right angles.
See Laczkovich, M. Tilings of polygons with similar triangles. Combinatorica, Vol 10, pp281-306. (1990).
The triangles must be one of three similarity classes with angles of (π/8, π/4, 5π/8), (π/4, π/3, 5π/12) or (π/12, π/4, 2π/3).
Examples of these have not been produced since examples with a small number of triangles are
|Smallest angle (degrees)||Number of triangles||Link