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