A meditation on Kepler's Aa
Craig S. Kaplan
A meditation on Kepler's Aa.
2006: Mathematical Connections in Art, Music and Science
pages 465-472, 2006.
Kepler's Harmonice Mundi includes a mysterious arrangement
of polygons labeled Aa, in which many of the polygons have fivefold
In the twentieth century, solutions were proposed for
how Aa might be continued in a natural way to tile the whole plane.
I present a collection of variations on Aa, and show how it forms one
step in a sequence of derivations starting from a simpler tiling.
I present alternate arrangements of the tilings based on spirals and
substitution systems. Finally, I show some Islamic star patterns
that can be derived from Kepler-like tilings.