Pythagorean Tiling

The pattern can be made with the following PolygonR&D program

go{
 scale 0.4
 right
 scale 2.5   
 right
 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.