Most of us have by now decked their houses for Christmas. But, if you haven't done so yet or if you're looking for something unusual for your Christmas tree or have time on your hands as new lockdowns during the festive season have prevented you from getting reunited with your dear ones, try and get inspired by the illustrations featured in the book De Divina Proportione (About the Divine Proportion, 15th century).
Written by the mathematician Luca Pacioli in the vulgar language around 1498 in Milan and first printed in 1509, the book studies in its first part the golden ratio from the perspective of mathematical proportions, pondering on its applications to geometry, visual art and architecture and discusses the ideas of Vitruvius (from his De Architectura), comparing the proportions of the human body to those of artificial structures, with examples from classical Greco-Roman architecture.
Pacioli, who credited Fibonacci as the main source for the mathematics he presented, shared his interest in the study of proportion with Piero della Francesca and indeed some of the content of this book (the third part) is a translation into the Vulgar tongue of an earlier book by Piero della Francesca, De quinque corporibus regularibus (On [the] Five Regular Solids). Pacioli actually doesn't credit him, but seems to plagiarise Piero della Francesca.
Leonardo Da Vinci drew the sixty illustrations of solids in colour that complete the book, drawings that look extremely fascinating for their perspectives. The drawings go from spheres to a polyedron with 72 faces, passing through three-dimensional polyhedra with opaque faces or hollow polyedra.
In the illustrations the polyhedra are suspended in space, as if they were hanging from a thread, almost to prove they come from the divine sphere, yet they are also characterised by a precise volumetric density so that their divine essence is somehow materialised or corporalised.
For your decorations you may want to try and reproduce the basic five solids - tetrahedron, hexahedron, icosahedron, octahedron and dodecahedron - or opt for more complex polyedra such as the hollow hexahedron or the stellated dodecahedron.
If you have a 3D printer or a 3D printing pen it may be easier to recreate some of these figures, but a basic material such as paper will provide you with endless fun and with rather unique Christmas decorations or with interesting elements for rather original accessories (remember Prada's geometrical earrings from the S/S 16 collection).
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