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.svg) |
(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.Referenced on Wolfram|Alpha
Triangle Tiling
Cite this as:
Weisstein, Eric W. "Triangle Tiling."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriangleTiling.html
Subject classifications
