Water, the icosahedron, flows out of one's hand when picked up, as if it is made of tiny little balls. Air is made of the octahedron its minuscule components are so smooth that one can barely feel it. There was intuitive justification for these associations: the heat of fire feels sharp and stabbing (like little tetrahedra). Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. in which he associated each of the four classical elements ( earth, air, water, and fire) with a regular solid. Plato wrote about them in the dialogue Timaeus c.360 B.C. The Platonic solids are prominent in the philosophy of Plato, their namesake. In any case, Theaetetus gave a mathematical description of all five and may have been responsible for the first known proof that no other convex regular polyhedra exist. Other evidence suggests that he may have only been familiar with the tetrahedron, cube, and dodecahedron and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. Some sources (such as Proclus) credit Pythagoras with their discovery. The ancient Greeks studied the Platonic solids extensively. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vertices of the dodecahedron, and the arrangement of the knobs was not always symmetric. The Platonic solids have been known since antiquity. Assignment to the elements in Kepler's Mysterium Cosmographicum
0 kommentar(er)
