Conway's Pinwheel Tiling
3 days ago
- #tiling
- #mathematics
- #geometry
- John Conway discovered a right triangle that can be partitioned into five similar triangles with sides in proportion 1 : 2 : √5.
- The process of making a larger similar triangle by using the entire triangle as the central (green) triangle of a new triangle creates an aperiodic tiling of the plane.
- Charles Radin was the first to describe the tiling in a publication, attributing it to Conway.
- An alternate visualization involves imagining the smallest triangles as a constant size and viewing the process from further away, with the outer triangle appearing constant in size but growing to cover the plane.
- An animated GIF illustrates the process of subdividing the triangle to form the tiling.
- A PostScript signature by John Tromp outputs a pinwheel tiling, showcasing the mathematical concept visually.