http://de.evo-art.org/index.php?action=history&feed=atom&title=Artwork_Inspired_by_Dual_Dodecahedra_and_Icosahedra 2026-09-02T02:07:03Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Artwork_Inspired_by_Dual_Dodecahedra_and_Icosahedra&diff=33255&oldid=prev 2017-12-06T18:09:01Z

<p>Die Seite wurde neu angelegt: „ == Referenz == Stephen Wassell and Mark Reynolds: <a href="/index.php?title=Artwork_Inspired_by_Dual_Dodecahedra_and_Icosahedra" title="Artwork Inspired by Dual Dodecahedra and Icosahedra">Artwork Inspired by Dual Dodecahedra and Icosahedra</a>. In: <a href="/index.php?title=Bridges_2017" title="Bridges 2017">Bridges 2017</a>, Pages 125–130. == DOI ==…“</p> <p><b>Neue Seite</b></p><div><br /> == Referenz == <br /> Stephen Wassell and Mark Reynolds: [[Artwork Inspired by Dual Dodecahedra and Icosahedra]]. In: [[Bridges 2017]], Pages 125–130. <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> A long-standing collaboration between an artist and a mathematician bears new fruit in the form of novel geometric constructions and several works of art based on them. The inspiration for the present collaboration is a recent result on the edge-length ratios between dual regular dodecahedra and icosahedra, specifically the two vertex-to-face pairings of these dual Platonic solids: when the icosahedron circumscribes the dodecahedron, the edge-length ratio is 𝜙/3, and conversely, when the dodecahedron circumscribes the icosahedron, the edge-length ratio is 𝜙2/√5, where 𝜙 is the golden number. These two edge-length ratios are the basis for the geometric constructions and the resulting artwork, which highlight interesting characteristics of the two ratios, both individually and as they relate to each other. <br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> @inproceedings{bridges2017:125,<br /> author = {Stephen Wassell and Mark Reynolds},<br /> title = {Artwork Inspired by Dual Dodecahedra and Icosahedra},<br /> pages = {125--130},<br /> booktitle = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},<br /> year = {2017},<br /> editor = {David Swart, Carlo H. S\&#039;equin, and Krist\&#039;of Fenyvesi},<br /> isbn = {978-1-938664-22-9},<br /> issn = {1099-6702},<br /> publisher = {Tessellations Publishing},<br /> address = {Phoenix, Arizona},<br /> note = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-125.pdf}}<br /> }<br /> <br /> == Used References == <br /> [1] “MARK REYNOLDS: June 12 2015 – July 12 2015” (appeared in The New Yorker, July 6 &amp; 13, 2015, p. 16). Retrieved from http://www.newyorker.com/goings-on-about-town/art/mark-reynolds (as of January 17, 2017).<br /> <br /> [2] Branko Mitrović and Stephen R. Wassell, eds. Andrea Palladio: Villa Cornaro in Piombino Dese. New York: Acanthus Press. 2006.<br /> <br /> [3] Mark A. Reynolds. “Geometric and Harmonic Means and Progressions,” Nexus Network Journal, 3, n. 2, pp. 147–150. 2001.<br /> <br /> [4] Stephen R. Wassell. “Arithmetic, Geometric and Harmonic Sequences,” Nexus Network Journal, 3, n. 2, pp. 151–155. 2001.<br /> <br /> [5] Stephen R. Wassell and Samantha Benito. “Edge-length ratios between dual Platonic solids: a surprisingly new result involving the golden ratio,” The Fibonacci Quarterly, 50, n. 2, pp. 144–154. 2012.<br /> <br /> [6] Kim Williams, Lionel March, and Stephen R. Wassell, eds. The Mathematical Works of Leon Battista Alberti. Boston: Birkhäuser Verlag. 2010.<br /> <br /> <br /> == Links == <br /> <br /> === Full Text === <br /> http://archive.bridgesmathart.org/2017/bridges2017-125.pdf<br /> <br /> [[internal file]] <br /> <br /> <br /> === Sonstige Links ===</div>

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