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# plastic number

The plastic number is a little-known number that has much in common with the golden ratio in that it is closely linked to architecture and to aesthetics. The concept of the plastic number was first described by the Dutchman Hans van der Laan (1904-1991) in 1928, shortly after he had abandoned his architectural studies and become a novice monk, and has subsequently been explored by the English architect Richard Padovan (1935–). It is derived from a cubic equation, rather than a quadratic in the case of the golden ratio, and is intimately linked to two ratios, approximately 3:4 and 1:7, which van der Laan considered fundamental in the relationship between human perception and shape and form. These ratios, he believed, express 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.