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Triangle Tiling


TriangleTiling

A triangle tiling is a tiling of the plane by identical triangles. Any triangle tiles the plane (Wells 1991, p. 208).

TriangleTilings

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.
(1)

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).


See also

Equilateral Triangle, Rectangle Tiling, Tiling, Triangle, Triangle Counting, Triangle Packing

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References

Conway, J. H. and Guy, R. K. "How Many Triangles." In The Book of Numbers. New York: Springer-Verlag, pp. 83-84, 1996.Sloane, N. J. A. Sequence A002717/M3827 in "The On-Line Encyclopedia of Integer Sequences."Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 68-69 and 208, 1991.

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Triangle Tiling

Cite this as:

Weisstein, Eric W. "Triangle Tiling." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriangleTiling.html

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