Rectangle Tiling


The number of ways N(m,n) of finding a subrectangle with an m×n rectangle can be computed by counting the number of ways in which the upper right-hand corner can be selected for a given lower left-hand corner. For a lower left-hand corner with coordinates (i,j), there are (m-i)(n-j) possible upper right-hand corners, so


Equivalently, N(m,n) is the number of ways of picking two lines out of sets of m+1 and n+1 lines, giving

N(m,n)=(m+1; 2)(n+1; 2)

as before. Particular tilings are shown above for 2×2 and 2×3 rectangles.

See also

Perfect Rectangle, Rectangle, Triangle Tiling

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Stewart, I. "Squaring the Square." Sci. Amer. 277, 94-96, July 1997.

Referenced on Wolfram|Alpha

Rectangle Tiling

Cite this as:

Weisstein, Eric W. "Rectangle Tiling." From MathWorld--A Wolfram Web Resource.

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