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.
Smallest angle (degrees)Number of trianglesLink
29.6762330318link
457link
459link
4511link
29.6762330317link
17.47909857699link
13.171777083811link
34.30680512417link
42.3247448049link
43.89823576511link
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 not known.

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