http://de.evo-art.org/index.php?action=history&feed=atom&title=A_Sangaku_Revived 2026-04-10T11:57:53Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=A_Sangaku_Revived&diff=4109&oldid=prev 2015-01-30T11:17:57Z

<p>Die Seite wurde neu angelegt: „ == Reference == Zsófia Ruttkay: <a href="/index.php?title=A_Sangaku_Revived" title="A Sangaku Revived">A Sangaku Revived</a>. In: <a href="/index.php?title=Bridges_2008" title="Bridges 2008">Bridges 2008</a>. Pages 155–162 == DOI == == Abstract == In this paper we give an account on …“</p> <p><b>Neue Seite</b></p><div><br /> == Reference ==<br /> Zsófia Ruttkay: [[A Sangaku Revived]]. In: [[Bridges 2008]]. Pages 155–162 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> In this paper we give an account on our mathematical and visual explorations inspired by a sangaku.<br /> First we introduce sangakus – traditional Japanese mathematical tablets. Then we give four examples of our static<br /> contemporary variants. Finally, we discuss in detail how a fifth sangaku led us to simulate the growth of water<br /> lilies, as a means of visualizing the problem. This approach lead to the mathematical field of circle packing, and<br /> made it possible to experience the visually intriguing process with different settings of the algorithm.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> Sangaku from 1873, solved by 11 year old boy<br /> http://www.kurims.kyoto-u.ac.jp/~okamoto/sangaku/sangaku.html<br /> <br /> H. Fukagawa and D. Pedoe, Japanese temple geometry problems = Sangaku, Charles Babbage<br /> Research Centre, Winnipeg, Canada, 1989.<br /> <br /> T. Rothman, Japanese temple geometry, Scientific American, 5, 1998.<br /> <br /> H. Fukagawa and T. Rothman, Sacred Mathematics, to appear<br /> http://www.princeton.edu/main/news/archive/S15/04/04O77/index.xml<br /> <br /> Sangaku Diagrams and Kinetigrams:<br /> http://interactive-mathvision.com/PaisPortfolio/Sangaku/SangakuFrames.html<br /> <br /> Japanese mathematics: http://www.ballstructure.com/Japanese_Math/<br /> <br /> Map of Sangaku locations: http://www.wasan.jp/english/<br /> <br /> Photos of some tablets: http://www.sangaku.info/<br /> <br /> I. Peterson, Temple Circles, http://www.maa.org/mathland/mathtrek_4_23_01.html<br /> <br /> G. Hart, A Modern Day Sangaku http://www.georgehart.com/sangaku/<br /> <br /> Solution of the 4 sangakus (in Dutch) http://www.arsetmathesis.nl/arthesis/sangopl.pdf<br /> <br /> Monet: Les Nympéas, Paris, L’ensemble de l’Orangerie, http://www.musee-orangerie.fr/homes/home_id24799_u1l2.htm<br /> <br /> Kepler’s sphere packing problem, http://mathworld.wolfram.com/SpherePacking.html<br /> <br /> Kepler’s Conjecture, http://mathworld.wolfram.com/KeplerConjecture.html<br /> <br /> T. Tarnai, Packing of equal circles in a circle in: Structural Morphology: Toward the New Millenium, The University of Nottingham, Nottingham, UK, 217-224, 1997.<br /> <br /> Best known circle packing up to 2005: http://www.packomania.com/<br /> <br /> K. Stephenson, Circle Packing: A Mathematical Tale , Notices of the American Mathematical<br /> Society, 2003. http://www.ams.org/notices/200311/fea-stephenson.pdf<br /> <br /> P. G. Szabó, M. Cs. Markót, T. Csendes, E. Specht, L. G. Casado, I. García, New Approaches to<br /> Circle Packing in a Square. With Program Codes (Springer Optimization and Its Applications, Vol.<br /> 6). New York. 2007. Springer.<br /> <br /> Zs Ruttkay, The simulation program as Java applet: http://wwwhome.cs.utwente.nl/~zsofi/sangaku/SanSim.html<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2008/bridges2008-155.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2008/bridges2008-155.html</div>

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