Luca Pacioli’s (c.1445–1517) book ‘Divina proportione’ (written 1496–8, published 1509) is famous in the history of mathematical beauty, but mostly for the wrong reasons.

The term ‘divine proportion’ refers to Euclid's ‘extreme and mean ratio’, known since the late 18th century as the ‘golden ratio’: $1.61803\ldots:1$.

Pacioli's use of the term ‘divine’ **was not based upon aesthetic appreciation**.

Rather, he made a mystical identification of certain properties of the ratio with attributes of God. E.g., the incommensurability of the ratio = the indefinability and ineffability of God.

But Pacioli aesthetically admired the five regular polyhedra — the platonic solids — and the archimedean solids that he knew. In the dedication of ‘Divina proportione’ he wrote that hoped that his patron would see ‘their most sweet harmony’. He linked the aesthetic value of the solids to that of the sphere, from which he saw them as deriving. He seems to have placed special value on the ‘most noble’ dodecahedron.

In his portrait (attached), a dodecahedron sits on top of one of his books as a symbol of mathematical success. His diagram is part of the construction of the tetrahedron. A glass rhombicuboctahedron hangs behind him.

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#GoldenRatio #DivineProportion #MathematicalBeauty #MathArt #polyhedron #RegularSolid #PlatonicSolid