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Symmetry: Culture and Science

Publication date: 2013-07
Volume: 24 Pages: 451 - 462
ISSN: 0865-4824, 2226-1877
Publisher: The Board of the International Society for the Interdisciplinary Study of Symmetry

Author:

Huylebrouck, Dirk
Bartlett, Christopher

Keywords:

composition in painting, golden section, Le Corbusier, Science & Technology, Physical Sciences, Mathematics, Interdisciplinary Applications, Mathematics, 19 Studies in Creative Arts and Writing

Abstract:

Christopher Bartlett has been wrestling with the apparent significance of a 1:1.3… ratio rectangle since presenting a paper on a Fairfield Porter painting at Banff in 2005. He observed that a rectangle with this aspect ratio could be partitioned into the union of a similar rectangle (i.e., one having the same aspect ratio) and another rectangle that has the aspect ratio close to the golden ratio. However, the precise value of the aspect ratio of a rectangle that can be partitioned in such a way remained unknown. Here, a calculation and a construction of the value of the ratio are provided. Its approximate value is 1:1.35 and this proportion seems to have been the goal of several proportions related to architecture, such as the Dom Hans van der Laan’s ‘Plastic number’, Gérard Cordonnier’s ‘radian number’ or Rafael de la Hoz’s ‘Cordovan proportion’. Moreover, the construction method strongly reminds Le Corbusier search for ‘the right angle’, though co-author Bartlett was not aware of it: his focus is on well-known paintings, suggesting the use of a 1:1.35 ratio in structuring the geometry of their compositions.