http://de.evo-art.org/index.php?action=history&feed=atom&title=The_Meta-golden_Ratio_Chi 2026-04-18T14:07:02Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=The_Meta-golden_Ratio_Chi&diff=3834&oldid=prev 2015-01-27T14:01:12Z

<p>Die Seite wurde neu angelegt: „ == Reference == Dirk Huylebrouck: <a href="/index.php?title=The_Meta-golden_Ratio_Chi" title="The Meta-golden Ratio Chi">The Meta-golden Ratio Chi</a>. In: <a href="/index.php?title=Bridges_2014" title="Bridges 2014">Bridges 2014</a>. Pages 151–158 == DOI == == Abstract == Based on artistic interpret…“</p> <p><b>Neue Seite</b></p><div><br /> == Reference ==<br /> Dirk Huylebrouck: [[The Meta-golden Ratio Chi]]. In: [[Bridges 2014]]. Pages 151–158 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Based on artistic interpretations, art professor Christopher Bartlett (Towson University, USA) independently<br /> rediscovered a mathematical constant called the ‘meta-golden section’, which had been very succinctly<br /> described 2 years earlier by Clark Kimberling. Bartlett called it ‘the chi ratio’ and denoted it by  (the letter<br /> following , the golden section, in the Greek alphabet). In contrast to mathematician Kimberling, Bartlett<br /> motivated his finding on artistic considerations. They may be subject to criticism similar to the ‘golden ratio<br /> debunking’, but here we focus on showing that his chi ratio is interesting as a number as such, with pleasant<br /> geometric properties, just as the golden ratio. Moreover, Bartlett’s construction of proportional rectangles<br /> using perpendicular diagonals, which is at the basis of his chi ratio, has interesting references in architecture<br /> and in art.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] Bartlett, Christopher and Huylebrouck, Dirk (2008), ‘Porter’s golden section, experimentally’, Bridges<br /> conference, Leeuwarden (The Netherlands).<br /> <br /> [2] Bartlett, Christopher and Huylebrouck, Dirk (2013), ‘Art and Math of the 1.35 Ratio Rectangle’,<br /> Symmetry: Culture and Science, Vol. 24, Delft (The Netherlands).<br /> <br /> [3] Herz-Fischler, Roger, ‘Didactics: Proportions in the Architecture Curriculum’, Nexus Network<br /> Journal, http://www.emis.de/journals/NNJ/Didactics-RHF.html.<br /> <br /> [4] Herz-Fischler, Roger (2005), ‘The Home of Golden Numberism’, The Mathematical Intelligencer,<br /> Edition Winter, n° 27, p 67-71.<br /> <br /> [5] Huylebrouck, Dirk (2001), ‘The golden section as an optimal solution’, ISIS-S conference, Sydney,<br /> Australia.<br /> <br /> [6] Huylebrouck, Dirk (2002), ‘More true Applications of the Golden Number’, in The Golden Section,<br /> Nexus Network Journal on Architecture and Mathematics, Stephen R. Wassell (Ed.), 4-1, Kim Williams<br /> Books.<br /> <br /> [7] Huylebrouck, Dirk (2004), ‘Golden gray’, FORMA, Society for Science on Form, SCIPRESS, Tokyo,<br /> Japan.<br /> <br /> [8] Huylebrouck, Dirk (2004), ‘Simple-minded golden section examples’, 6th Interdisciplinary Symmetry<br /> Congress and Exhibition of ISIS, Tihany (Hungary).<br /> <br /> [9] Huylebrouck, Dirk (2004), ‘Simple golden section examples’, 6th Interdisciplinary Symmetry<br /> Congress and Exhibition of ISIS, Tihany (Hungary).<br /> <br /> [10] Huylebrouck, Dirk (2009), ‘Golden section atria’, ISIS-Symmetry conference, Wroclaw-Krakow<br /> (Poland).<br /> <br /> [11] de la Hoz, Rafael, ‘La proporción Cordobesa’, (1973), Actas de la quinta asamblea de instituciones<br /> de Cultura de las Diputaciones, Ed. Diputación de Córdoba.<br /> <br /> [12] Kimberling, Clark, ‘A Visual Euclidean Algorithm’, The Mathematics Teacher, 76 (1983) 108-109.<br /> <br /> [13] Markowsky, George (1992), ‘Misconceptions about the Golden Ratio’, The College Mathematics<br /> Journal, Vol. 23, No.1, January, p. 2-19.<br /> <br /> [14] Redondo Buitrago, Antonia (2013), ‘On the ratio 1.3 and related numbers’, Proceedings of 9th ISIS<br /> Congress Festival Symmetry: Art and Science. Palormo, Crete, Greece.<br /> <br /> [15] Sloane Neil, On-Line Encyclopedia of Integer Sequences, series A188635: http://oeis.org/A188635.<br /> <br /> [16] Sloane Neil, On-Line Encyclopedia of Integer Sequences, series A112576: http://oeis.org/A112576.<br /> <br /> [17] Wikipedia on van der Laan’s Plastic number: http://en.wikipedia.org/wiki/Plastic_number.<br /> <br /> [18] Wolfram Mathworld’s site on paper folding: http://mathworld.wolfram.com/Folding.html.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2014/bridges2014-151.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2014/bridges2014-151.html</div>

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