Saturday, September 30, 2006

Pythagorean Tiling

The pattern can be made with the following PolygonR&D program
scale 0.4
scale 2.5
sides 4
ifon none {
paint purple
4 {
create go
right }
} { }

This tiling often appears on many floors. It is made with two different sizes of square tiles. The sizes of tiles doesn't matter--they will always form a pattern without gaps. A related fact about this pattern is that it demonstrates a proof of the Pythagorean theorem. The combined area of a purple and a yellow square is the same area as one of the squares constructed by the grid to the left.

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