http://de.evo-art.org/index.php?action=history&feed=atom&title=The_Planar_Crystallographic_Groups_Represented_at_the_Alhambra 2026-05-03T07:41:20Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=The_Planar_Crystallographic_Groups_Represented_at_the_Alhambra&diff=3917&oldid=prev 2015-01-28T14:20:04Z

<p>Die Seite wurde neu angelegt: „ == Reference == B. Lynn Bodner: <a href="/index.php?title=The_Planar_Crystallographic_Groups_Represented_at_the_Alhambra" title="The Planar Crystallographic Groups Represented at the Alhambra">The Planar Crystallographic Groups Represented at the Alhambra</a>. In: <a href="/index.php?title=Bridges_2013" title="Bridges 2013">Bridges 2013</a>. Pages 225–232 == DOI == == Abs…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> B. Lynn Bodner: [[The Planar Crystallographic Groups Represented at the Alhambra]]. In: [[Bridges 2013]]. Pages 225–232 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> The geometric patterns that cover the walls, ceilings and floors of the Alhambra in Granada, Spain have<br /> been the subject of study by many mathematical researchers ever since 1944, when E. Müller first reported<br /> the number of distinct planar crystallographic groups found there. In subsequent years, the count has varied,<br /> sometimes due to inconsistencies in the ways in which the patterns were chosen and analyzed. As such,<br /> contradictions and controversy still surround the issue. After a brief introduction, this paper will provide the<br /> criteria used by this author in an on-site visit in 2003 in order to catalog different crystallographic groups<br /> represented by patterns in the Alhambra. Each group identified is illustrated by a representative pattern.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] E. A. Müller, Gruppentheoretische und Strukturanalytische Untersuchungen der Maurischen<br /> Ornamente aus der Alhambra in Granada, University of Zürich, 1944.<br /> <br /> [2] B. Grünbaum, A. Grünbaum, G. C. Shephard. Symmetry in Moorish and Other Ornaments. Comp. &amp;<br /> Maths with Applications, Vol. 12B, No. 3 / 4, pp. 641 – 653, 1986.<br /> <br /> [3] R. Perez-Gomez, The Four Regular Mosaics Missing in the Alhambra, Comput. Math. Applic., v. 14, no.<br /> 2, 1987, 133-137.<br /> <br /> [4] B. Grünbaum. What Symmetry Groups are Present in the Alhambra? Notices of the AMS, June/July<br /> 2006 issue (Volume 53, Number 6) and also available at http://www.ams.org/notices/200606/comm-grunbaum.pdf<br /> <br /> [5] W. K. Chorbachi. In the Tower of Babel: Beyond Symmetry in Islamic Art. Computers &amp; Mathematics<br /> with applications, Vol. 17b, pp. 751 – 189, (1989).<br /> <br /> [6] D. Schattschneider, The Plane Symmetry Groups: Their Recognition and Notation, Amer. Math.<br /> Monthly (85) 1978, 439 – 450.<br /> <br /> [7] D. K. Washburn and D.W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern<br /> Analysis. University of Washington Press, 1988.<br /> <br /> [8] S. J. Abas and A. S. Salman. Symmetries of Islamic Geometrical Patterns. World Scientific, 1998.<br /> <br /> [9] The Geometer’s Sketchpad software program, available at http://www.keypress.com.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2013/bridges2013-225.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2013/bridges2013-225.html</div>

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