Johannes Kepler was a German astronomer and mathematician ho discovered that planetary motion is elliptical. Early in his life, Kepler wanted to prove that the universe obeyed Platonistic mathematical relationships, such as the planetary orbits were circular and at distances from the sun proportional to the Platonic solids (see paragraph below). However, when his friend the astronomer Tycho Brahe died, he gave Kepler his immense collection of astronomical observations. After years of studying these observations, Kepler realized that his previous thought about planetary motion were wrong, and he came up with his three laws of planetary motion. Unfortunately, he did not have a unifying theory for these laws. This had to until Newton formulated his laws of gravity and motion.PLATONIC SOLIDSA platonic solid is a solid having similar, regular polygonal faces. There are five Platonic solids: the icosahedron, tetrahedron, octahedron, dodecahedron, and cube. They are characterized by the fact that each face is a straight-sided figure with equal sides and equal angles: Tetrahedron: 4 triangular faces, 4 vertices, 6 edges Cube: 6 square faces, 8 vertices, 12 edges Octahedron: 8 triangular faces, 6 vertices, 12 edges Dodecahedron: 12 pentagonal faces, 20 vertices, 30 edges Icosahedron: 20 triangular faces, 12 vertices, 30 edgesMany people wonder why there should be exactly five Platonic solids, and whether there is one that has not been found yet. However, it is easy show that there must be five and that there cannot be more than five. At each vertex, at least three faces must come together, because if only two came together they would collapse against one another and a solid would not be created. Secondly, the sum of the interior angles of the faces meeting at each vertex must be less than 360, because if they didn't, they would not all fit together. Each interior angle of an equilateral triangle is 60, therefore we could fi...
