## The Greeks Kepler and the Five Elements

The Greeks saw great significance in the existence of just 5 Platonic solids and they related them to the 4 ELEMENTS (fire, earth, air and water) that they thought everything was made from. Together with the UNIVERSE, they associated each with a particular solid.

The astronomer and mathematician, Kepler (1571-1630), shown here as a link to the History of Mathematics web site at St Andrews University, Scotland, justified this as follows:

Of the 5 solids, the tetrahedronhas the smallest volume for its surface area and the icosahedronthe largest; they therefore show the properties of drynessand wetnessrespectively and so correspond to FIRE and WATER.

The cube, standing firmly on its base, corresponds to the stable EARTH but the octahedronwhich rotates freely when held by two opposite vertices, corresponds to the mobile AIR. The dodecahedroncorresponds to the UNIVERSE because the zodiac has 12 signs (the constellations of stars that the sun passes through in the course of one year) corresponding to the 12 faces of the dodecahedron.

Kepler called the golden section "the division of a line into extreme and mean ratio", as did the Greeks. He wrote the following about it:

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