The Divine Proportion, also known as the Golden Ratio, is equal to:
(5½+1)/2
or as a decimal:
1.61803398874989484820458683436563811772030917980576...
Euclid13 in his book Elements used this ratio to construct first a3 regular pentagon, then following this the dodecahedron and the icosahedron. This ratio was also important to the Egyptians, as even the Rhind papyrus refers to a 'sacred ratio' and the ratio in the Great Pyramid at Gizeh4,9 of an altitude of a face stack8 to half the side of the base11 is almost exactly 1.618.
Leonardo da Vinci refered to it6 as the 'sectio aurea', the Golden Section. Renaissance artists regularly used the Golden Section in dividing the surface of a painting into proportions pleasing to the eye. Likewise architects use this ratio to create proportions of a building. In fact, the first Italian edition of Vitruvius' De Architectura uses the Golden Ratio to analyse the elevation of the Milan Cathedral.
Using the Divine Proportion, one can create a rectangle whose sides follow this ratio. It is possible to draw5,7 an equiangular spiral through successive vertices of the sequence of rectangles. The spiral2 tends towards the point where the diagonals of all the Golden Rectangles meet. Not surprising12, this spiral1 appears regularly in nature... in the arrangement of sunflower heads, spiral10 shells and the arrangement of leaves on branches.
From Stonehenge to the Acropolis, Chichen Itza to the Cathedral of Chartres, and the Vitruvian Man to Michelangelo's David14, the Divine Proportion ratio has shown itself time and time again throughout history.
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