Hey, kudos!
You don't run arbitrary scripts either!

My apologies for the JS on this page…
it's prettify.js for syntax highlighting
in code blocks. I've added one line of
CSS for you; the rest of this site
should work fine.

      ♥Ⓐ isis

code.

Other articles


  1. Platonic Solids in Nature


    Platonic solids, or regular convex polyhedra, are named after the Greek philosopher Plato who theorized that the five classical elements (Empedocles’ wind, water, fire, and earth, with an added element for spirit) were actually comprised of regular polyhedra. They are five in number and named for the number of faces they exhibit. They are: the tetrahedron, the hexahedron, the octahedron, the dodecahedron, and the icosahedron. Platonic solids have been the metaphysical and aesthetic inspiration of geometers for thousands of years. Johannes Kepler, a 17^th^ century German mathematician, astronomer, and astrologist, detailed a theory in which the relational distances between the planetary orbits is given by circumscribing the platonic solids within spheres. “In Mysterium Cosmographicum, published in 1596, Kepler laid out a model of the solar system in which the five solids were set inside one another and separated by a series of inscribed and circumscribed spheres. The six spheres each corresponded to one of the planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). The solids were ordered with the innermost being the octahedron, followed by the icosahedron, dodecahedron, tetrahedron, and finally the cube. In this way the structure of the solar system and the distance relationships between the planets was dictated by the Platonic solids. In the end, Kepler’s original idea had to be abandoned, but out of his research came the recognition that the orbits of planets are ellipses rather than circles, as well as his two laws of orbital dynamics, changing the courses of physics and astronomy, plus the discovery of the Kepler solids.”^1^

    Plato wrote about these polyhedra in the dialogue Timaeus c.360 B.C. in which he associated each of the four classical elements with a regular solid. Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. There was intuitive justification for these associations: the heat of fire feels sharp and stabbing (like little tetrahedra). Air is made of the octahedron; its minuscule components are so smooth that one can barely feel it. Water, the icosahedron, flows out of one’s hand when picked up, as if it is made of tiny little balls. By contrast, a highly un-spherical solid, the hexahedron (cube) represents earth. These clumsy little solids cause dirt to crumble and break when picked up, in stark difference to the smooth flow of water. Moreover, the solidity of the Earth was believed to be due to the fact that the cube is the only regular solid that tesselates Euclidean space. The fifth Platonic solid, the dodecahedron, Plato obscurely remarks, “…the god used for arranging the constellations on the whole heaven”. Aristotle added a fifth element, aithêr (aether in Latin, “ether” in English) and postulated that the heavens were made of this element, but he had no interest in matching it with Plato’s fifth solid.

    Platonic solids occur frequently in nature. Their forms are the complex crystalizations of minerals and appear as the skeletal remains of several species of …

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