Abstract. Richard Padovan presents the plastic number, a system of proportion discovered by Dom Hans Van Der Laan, at the Nexus 2002 conference in Obidos, Portugal, 15-18 June 2002. The full text of this paper is available in the book Nexus IV: Architecture and Mathematics.

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Dom Hans Van Der Laan And The Plastic Number

Richard Padovan
28 Petersham Road
Richmond upon Thames
Surrey TW10 6UW UK

The plastic number, discovered by Dom Hans van der Laan (1904-91) in 1928 shortly after he had abandoned his architectural studies and become a novice monk, differs from all previous systems of architectural proportions in several fundamental ways. Its derivation from a cubic equation (rather than a quadratic one such as that which defines the golden section) is a response to the three-dimensionality of our world. It is truly aesthetic in the original Greek sense, i.e., its concern is not 'beauty' but clarity of perception. Its basic ratios, approximately 3:4 and 1:7, are determined by the lower and upper limits of our normal ability to perceive differences of size among three-dimensional objects. The lower limit is that at which things differ just enough to be of distinct types of size. The upper limit is that beyond which they differ too much to relate to each other; they then belong to different orders of size. According to Van der Laan, these limits are precisely definable. The mutual proportion of three-dimensional things first becomes perceptible when the largest dimension of one thing equals the sum of the two smaller dimensions of the other. This initial proportion determines in turn the limit beyond which things cease to have any perceptible mutual relation. Proportion plays a curcial role in generating architectonic space, which comes into being through the proportional relations of the solid forms that delimit it. Architectonic space might therefore be described as a proportion between proportions.

The order of size embraces seven consecutive types contained between eight measures

Born in 1935, Richard Padovan studied architecture at the Architectural Association, London (1952-57). Since then he has combined practice with teaching and writing on architecture. He believes, however, that his real architectural education began when in encountered the work and thought of the Dutch Benedictine architect Dom Hans van der Laan in 1974. His translation of Van der Laan's treatise Architectonic Space appeared in 1983, followed by a monograph, Dom Hans van der Laan, Modern Primitive, in 1994. In 1999 he published Proportion: Science, Philosophy, Architecture. His latest book, Towards Universality: Le Corbusier, Mies and De Stijl (2002), contrasts the grandiose philosophical ideals of European modernism with its failure to realize those aims, particularly in the building of cities.

 The correct citation for this article is:
Richard Padovan, "Dom Hans Van Der Laan and the Plastic Number", pp. 181-193 in Nexus IV: Architecture and Mathematics, eds. Kim Williams and Jose Francisco Rodrigues, Fucecchio (Florence): Kim Williams Books, 2002. http://www.nexusjournal.com/conferences/N2002-Padovan.html

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