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Golden section(ism): From mathematics to the theory of art and musicology, Part 1. (English) Zbl 0979.91504

Summary: The golden section, \(a/b=b/(a+b)\), can be considered in both space and time (Chap. 1). We survey this concept in mathematics and art, including the terms “extreme and mean ratio” (Greek mathematics), “propertion of a middle and two ends” (Islamic mathematics), “divine proportion” (Pacioli, 15th c.), “divine section” (Kepler, 17th c.), “golden section” (19 th c.), and some widespread misunderstandings in the literature (Chap. 2). Among others, we demonstrate that the surviving documents on the proportional systems of Polykleitos, Vitruvius, and Dürer, respectively, cannot refer to the golden section, despite the fact that very many authors claim that this concept is clearly used by them. We present our new interpretation of the Leonardo-Pacioli cooperation with the conclusion that Leonardo’s “divine propotion” is a metaphorical expression without a specific meaning, which was later adopted as a mathematical term for the golden section by Pacioli.

MSC:

91F99 Other social and behavioral sciences (mathematical treatment)

Keywords:

golden section
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