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<p>Die Seite wurde neu angelegt: „ == Reference == Douglas Dunham: <a href="/index.php?title=More_%22Circle_Limit_III%22_Patterns" title="More &quot;Circle Limit III&quot; Patterns">More &quot;Circle Limit III&quot; Patterns</a>. In: <a href="/index.php?title=Bridges_2006" title="Bridges 2006">Bridges 2006</a>. Pages 451–458 == DOI == == Abstract == M.C. Escher used the…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Douglas Dunham: [[More &quot;Circle Limit III&quot; Patterns]]. In: [[Bridges 2006]]. Pages 451–458 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> M.C. Escher used the Poincar ́e model of hyperbolic geometry when he created his four “Circle Limit” patterns. The<br /> third one of this series, Circle Limit III, is usually considered to be the most attractive of the four. In Circle Limit<br /> III, four fish meet at right fin tips, three fish meet at left fin tips, and three fish meet at their noses. In this paper, we<br /> show patterns with other numbers of fish that meet at those points, and describe some of the theory of such patterns.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] Anonymous, On the Cover, Mathematical Intelligencer, 18, No. 4 (1996), p. 1.<br /> <br /> [2] H.S.M. Coxeter, Crystal symmetry and its generalizations, Royal Society of Canada, (3), 51 (1957),<br /> pp. 1–13.<br /> <br /> [3] H.S.M. Coxeter, The Non-Euclidean Symmetry of Escher’s Picture ‘Circle Limit III’, Leonardo, 12<br /> (1979), pp. 19–25.<br /> <br /> [4] H.S.M. Coxeter. The trigonometry of Escher’s woodcut ”Circle Limit III”, Mathematical Intelligencer, 18, No. 4 (1996), pp. 42–46. This his been reprinted by the American Mathematical Society<br /> at: http://www.ams.org/featurecolumn/archive/circle_limit_iii.html and also in<br /> M.C. Escher’s Legacy: A Centennial Celebration, D. Schattschneider and M. Emmer editors, Springer Verlag, New York, 2003, pp. 297–304.<br /> <br /> [5] D. Dunham, Hyperbolic Art and the Poster Pattern: http://www.mathaware.org/mam/03/essay1.html, on the Mathematics Awareness Month 2003 web site: http://www.mathaware.org/mam/03/.<br /> <br /> [6] B. Ernst, The Magic Mirror of M.C. Escher, Benedikt Taschen Verlag, Cologne, Germany, 1995. ISBN<br /> 1886155003<br /> <br /> [7] M. Greenberg, Euclidean &amp; Non-Euclidean Geometry, Third Edition: Development and History, 3nd<br /> Ed., W. H. Freeman, Inc., New York, 1993. ISBN 0716724464<br /> <br /> [8] D. Schattschneider, M.C. Escher: Visions of Symmetry, 2nd Ed., Harry N. Abrams, Inc., New York,<br /> 2004. ISBN 0-8109-4308-5<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2006/bridges2006-451.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2006/bridges2006-451.html</div>

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