http://de.evo-art.org/index.php?action=history&feed=atom&title=In_Search_of_Demiregular_Tilings 2026-05-16T20:25:46Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=In_Search_of_Demiregular_Tilings&diff=4158&oldid=prev 2015-01-30T21:03:31Z

<p>Die Seite wurde neu angelegt: „ == Reference == Helmer Aslaksen: <a href="/index.php?title=In_Search_of_Demiregular_Tilings" title="In Search of Demiregular Tilings">In Search of Demiregular Tilings</a>. In: <a href="/index.php?title=Bridges_2006" title="Bridges 2006">Bridges 2006</a>. Pages 533–536 == DOI == == Abstract == Many books on mathe…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Helmer Aslaksen: [[In Search of Demiregular Tilings]]. In: [[Bridges 2006]]. Pages 533–536 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Many books on mathematics and art discuss a topic called demiregular tilings and claim that there are 14 such tilings.<br /> However, many of them give different lists of 14 tilings! In this paper we will compare the lists from some standard<br /> references that give a total of 18 such tilings. We will also show that unless we add further restrictions, there will<br /> in fact be infinitely many such tilings. The “fact” that there are 14 demiregular tilings has been repeated by many<br /> authors. The goal of this paper is to put an end to the concept of demiregular tilings.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] D. P. Chavey, Periodic tilings and tilings by regular polygons, Ph.D. thesis, Univ. of Wisconsin, Madi-<br /> son, 1984.<br /> <br /> [2] Keith Critchlow, Order in Space, A Design Source Book, Thames and Hudson, 1969.<br /> <br /> [3] Brian L. Galebach, Number of n-uniform tilings, The On-Line Encyclopedia of Integer Sequences,<br /> http://www.research.att.com/~njas/sequences/A068599.<br /> <br /> [4] Brian L. Galebach, N-uniform Tilings, http://probabilitysports.com/tilings.html.<br /> <br /> [5] Matila Ghyka, The Geometry of Art and Life, Sheed and Ward, 1946 (second edition, Dover Publica-<br /> tions, 1977).<br /> <br /> [6] Branko Grünbaum and G.C. Shephard, Tilings by Regular Polygons, Mathematics Magazine 50 (1977),<br /> 227–247.<br /> <br /> [7] Branko Grünbaum and G.C. Shephard, Tilings and Patterns, W. H. Freeman and Company, 1987.<br /> <br /> [8] O. Krötenheerdt, Die homogenen Mosaike n-ter Ordnung in der euklidischen Ebene. I, Wiss. Z. Martin-<br /> Luther-Univ. Halle-Wittenberg, Math.-Natur. Reihe 18 (1969), 273–290.<br /> <br /> [9] Miranda Lundy, Sacred Geometry, Walker and Company, 2001.<br /> <br /> [10] NG Lay Ling, Tilings and Patterns, Honours Project, Department of Mathematics, National Univ. of<br /> Singapore, 2004, http://www.math.nus.edu.sg/aslaksen/projects/nll.pdf.<br /> <br /> [11] Hugo Steinhaus, Mathematical Snapshots, Dover Publications, 1999 (originally published in Polish,<br /> 1937; first English edition, 1938; Oxford University Press, 1950).<br /> <br /> [12] Eric W. Weisstein, Demiregular Tessellation, from MathWorld — A Wolfram Web Resource, mathworld.<br /> wolfram.com/DemiregularTessellation.html.<br /> <br /> [13] Robert Williams, The Geometrical Foundation of Natural Structure: A Source Book of Design, Dover<br /> Publications, 1979.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2006/bridges2006-533.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2006/bridges2006-533.html</div>

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