The Conway Tessellation
Let be the right triangle with side length, and . Conway noticed that can be divided in five isometric copies of its image by the dilation of factor .
By suitably rescaling and translating/rotating, this operation can be iterated to obtain an infinite increasing sequence of growing triangles all made of isometric copies of . The union of all these triangles yields a tiling of the whole plane by isometric copies of .
In this tiling, isometric copies of appears in infinitely many orientations (this is due to the angles and of, both non-commensurable with ). Despite of this, all the vertices have rational coordinates.
Read more about this topic: Pinwheel Tiling
Famous quotes containing the word conway:
“Gentlemen, I give you a toast. Here’s my hope that Robert Conway will find his Shangri-La. Here’s my hope that we all find our Shangri-La.”
—Robert Riskin (1897–1955)