Alan J. CainThe idea that the ‘golden’ ratio — $1.61803\ldots:1$ — has applications in visual art and architecture does not go back any further than the 2nd edition (1799–1802) of Jean-Étienne Montucla's (1725–99) (generally superb) ‘Histoire des Mathématiques’, in which he made the **incorrect** statement that Luca Pacioli's (c.1447–1517) book ‘Divina Proportione’ included illustrations of the ratio's application to architecture and font design.
This was shortly after the earliest known appearance of the term ‘golden section’ in Johann Samuel Traugott Gehler’s (1751–95) general scientific dictionary ‘Physikalisches Wörterbuch’.
The golden ratio was then taken up by Adolph Zeising (1810–76) as the basis for a system of aesthetic proportion in his book ‘New Theory of the Proportions of the Human Body’ (1854), where he argued — apparently to his own satisfaction — that his system agreed with the proportions of many masterpieces of art.
The psychologist Gustav Fechner (1801–87) made a much-misreported experiment in which people were asked to choose the most aesthetically pleasing of various rectangles (shown in the attached image). The most popular choice was the 34 ∶ 21 rectangle, whose proportions approximate the golden ratio. Fechner's conclusion was only that **a range of rectangles**, including the golden ratio rectangle, were considered most pleasing.
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#GoldenRatio #GoldenSection #DivineProportion #HistMath #aesthetics #Zeising #Fechner
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