The Plastic Brain

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scipsy:

The formula 1+2+3+…+n = k2 holds for only certain values of n and k.

The first solution n=1 k=1 is trivial.

The next solution is n=8 k=6. The following pictures show polyominoes of length 1-8 tiled inside a 6 x 6 square, one with L polyominoes, and the other with W polyominoes:

Tiling Squares with Arithmetic Polyominoes

For more information on the fascinating world of polyominoes, see:

http://mathworld.wolfram.com/Polyomino.html

And don’t even get me started on the r-pentomino from Conway’s Game of Life.

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Author: Rogan Tinsley

Biology, science and maths teacher with a PhD in Neuroscience and passion for education.

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