Triangle Tiling
A triangle tiling is a tiling of the plane by identical triangles. Any triangle tiles the plane (Wells 1991, p. 208).
The total number of triangles (including inverted ones) in the above figures are given by
![N(n)={1/8n(n+2)(2n+1) for n even; 1/8[n(n+2)(2n+1)-1] for n odd.](/images/equations/TriangleTiling/NumberedEquation1.gif) |
(1)
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The first few values are 1, 5, 13, 27, 48, 78, 118, 170, 235, 315, 411, 525, 658, 812, 988, 1188, 1413, 1665, ... (OEIS A002717).
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triangle tiling
