http://de.evo-art.org/index.php?action=history&feed=atom&title=A_Meditation_on_Kepler%27s_AaA Meditation on Kepler's Aa - Versionsgeschichte2026-05-16T20:28:36ZVersionsgeschichte dieser Seite in de_evolutionary_art_orgMediaWiki 1.27.4http://de.evo-art.org/index.php?title=A_Meditation_on_Kepler%27s_Aa&diff=4146&oldid=prevGbachelier: Die Seite wurde neu angelegt: „== Reference == Craig S. Kaplan: A Meditation on Kepler's Aa. In: Bridges 2006. Pages 465–472 == DOI == == Abstract == Kepler’s Harmonice M…“2015-01-30T20:24:54Z<p>Die Seite wurde neu angelegt: „== Reference == <a href="/index.php?title=Craig_S._Kaplan" title="Craig S. Kaplan">Craig S. Kaplan</a>: <a href="/index.php?title=A_Meditation_on_Kepler%27s_Aa" title="A Meditation on Kepler's Aa">A Meditation on Kepler's Aa</a>. In: <a href="/index.php?title=Bridges_2006" title="Bridges 2006">Bridges 2006</a>. Pages 465–472 == DOI == == Abstract == Kepler’s Harmonice M…“</p>
<p><b>Neue Seite</b></p><div>== Reference ==<br />
[[Craig S. Kaplan]]: [[A Meditation on Kepler's Aa]]. In: [[Bridges 2006]]. Pages 465–472 <br />
<br />
== DOI ==<br />
<br />
== Abstract ==<br />
Kepler’s Harmonice Mundi includes a mysterious arrangement of polygons labeled Aa, in which many of the poly-<br />
gons have fivefold symmetry. In the twentieth century, solutions were proposed for how Aa might be continued in a<br />
natural way to tile the whole plane. I present a collection of variations on Aa, and show how it forms one step in a<br />
sequence of derivations starting from a simpler tiling. I present alternate arrangements of the tilings based on spirals<br />
and substitution systems. Finally, I show some Islamic star patterns that can be derived from Kepler-like tilings.<br />
<br />
== Extended Abstract ==<br />
<br />
== Bibtex == <br />
<br />
== Used References ==<br />
[1] Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy. Unsolved Problems in Geometry. Springer-<br />
Verlag, 1991.<br />
<br />
[2] L. Danzer, B. Gr ̈unbaum, and G. C. Shephard. Can all tiles of a tiling have five-fold symmetry? Amer-<br />
ican Mathematical Monthly, 89:568–585, 1982.<br />
<br />
[3] Branko Gr ̈unbaum and G. C. Shephard. Tilings and Patterns. W. H. Freeman, 1987.<br />
<br />
[4] Craig S. Kaplan. Computer Graphics and Geometric Ornamental Design. PhD thesis, Department of<br />
Computer Science & Engineering, University of Washington, 2002.<br />
<br />
[5] Craig S. Kaplan. Islamic star patterns from polygons in contact. In Proceedings of the 2005 conference<br />
on graphics interface. Canadian computer human communication society, 2005.<br />
<br />
[6] Roger Penrose. Pentaplexity. Mathematical Intelligencer, 2:32–37, 1979/80.<br />
<br />
[7] John Savard. Pentagonal tilings. http://www.quadibloc.com/math/penint.htm<br />
<br />
<br />
== Links ==<br />
=== Full Text === <br />
http://archive.bridgesmathart.org/2006/bridges2006-465.pdf<br />
<br />
[[intern file]]<br />
<br />
=== Sonstige Links ===<br />
http://archive.bridgesmathart.org/2006/bridges2006-465.html</div>Gbachelier