Golden Ratio,Later Influence

Golden Ratio

"For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean—then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one" (31c - 32a); thereby he implies the aesthetically perfect proportion known as Golden ratio or Golden mean


Later influence

Medieval manuscript of Calcidius' Latin Timaeus translation.The Timaeus was translated into Latin by Cicero,[6] and the first part (to 53c) was again translated by Calcidius circa 321 AD. Calcidius' partial translation of the Timaeus was the only Platonic dialogue, and one of the few works of classical natural philosophy, available to Latin readers in the early Middle Ages. Thus it had a strong influence on medieval Neoplatonic cosmology and was commented on particularly by 12th century Christian philosophers of the Chartres School, such as Thierry of Chartres and William of Conches, who interpreting it in the light of the Christian faith understood the dialogue to refer to a creatio ex nihilo.[7]

composition of the four elements Timaeus

The ElementsTimaeus claims that the minute particle of each element had a special geometric shape: tetrahedron (fire), octahedron (air), icosahedron (water), and cube (earth).






Tetrahedron (fire) Octahedron (air) Icosahedron (water) Cube (earth)



The Timaeus makes conjectures on the composition of the four elements which some ancient Greeks thought constituted the physical universe: earth, water, air, and fire. Timaeus links each of these elements to a certain Platonic solid: the element of earth would be a cube, of air an octahedron, of water an icosahedron, and of fire a tetrahedron.[5] Each of these perfect polyhedra would be in turn composed of trianagular faces the 30-60-90 and the 45-45-90 triangles. The faces of each element could be broken down into its component right-angled triangles, either isosceles or scalene, which could then be put together to form all of physical matter. Particular characteristics of matter, such as water's capacity to extinguish fire, was then related to shape and size of the constituent triangles. The fifth element (i.e. Platonic solid) was the dodecahedron, whose faces are not triangular, and which was taken to represent the shape of the Universe as a whole, possibly because of all the elements it most approximates a sphere, which Timaeus has already noted was the shape into which God had formed the Universe..



The extensive final part of the dialogue addresses the creation of humans, including the soul, anatomy, perception, and transmigration of the soul.