Quelltext der Seite A Meditation on Kepler's Aa

== Reference ==
[[Craig S. Kaplan]]: [[A Meditation on Kepler's Aa]]. In: [[Bridges  2006]]. Pages 465–472 

== DOI ==

== Abstract ==
Kepler’s Harmonice Mundi includes a mysterious arrangement of polygons labeled Aa, in which many of the poly-
gons have fivefold symmetry. 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.

== Extended Abstract ==

== Bibtex == 

== Used References ==
[1] Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy. Unsolved Problems in Geometry. Springer-
Verlag, 1991.

[2] L. Danzer, B. Gr ̈unbaum, and G. C. Shephard. Can all tiles of a tiling have five-fold symmetry? Amer-
ican Mathematical Monthly, 89:568–585, 1982.

[3] Branko Gr ̈unbaum and G. C. Shephard. Tilings and Patterns. W. H. Freeman, 1987.

[4] Craig S. Kaplan. Computer Graphics and Geometric Ornamental Design. PhD thesis, Department of
Computer Science & Engineering, University of Washington, 2002.

[5] Craig S. Kaplan. Islamic star patterns from polygons in contact. In Proceedings of the 2005 conference
on graphics interface. Canadian computer human communication society, 2005.

[6] Roger Penrose. Pentaplexity. Mathematical Intelligencer, 2:32–37, 1979/80.

[7] John Savard. Pentagonal tilings. http://www.quadibloc.com/math/penint.htm


== Links ==
=== Full Text === 
http://archive.bridgesmathart.org/2006/bridges2006-465.pdf

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=== Sonstige Links ===
http://archive.bridgesmathart.org/2006/bridges2006-465.html