Johannes Kepler

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Johannes Kepler
Johannes Kepler was born on December 27, 1571, a premature child. He was born in Weil, in Swabia, a wine region in Southwest Germany not far from France. Kepler waent to the University of Tuebingen, a Protestant institution, where he studied mainly theology and philosophy, but also mathematics and astronomy. After Kepler graduated from Tuebingen, he was offered a professorship of astronomy in faraway Graz, Styria where he went in 1954. One of the duties of this Professorship was to make astrological predictions. While lecturing to his math class in Graz, contemplating some geometric figure involving Concentric Circles and triangles on the backboard, Kepler suddenly realized that figures of the type shown here determine a definite fixed ratio between the sizes of the two circles, provided the triangle has all sides equal, and a different ratio between the sizes will occur for a square between the two cirtcles, another for a regular pentagon. He really believed in the Copernicah System, so he saw the planetary orbits as six concentric circles. He felt the universe would somehow show mathematical beauty of symmetry. He suggested that the orbits might be arranged so that regular polygons would just fit between adjacent ones, and maybe somehow this reflected some invisible underlying structure holding it all together. Disappointingly, he found it just didn’t work the ratio’s where wrong. Then he had another inspiration. The universe was three-dimensional, and instead of thinking about circles, he should be thinking about spheres, with the planetary orbits along the equators. The anologue would be two concentric spheres with a tetrahedron between them, so that the outer sphere passes through the verticles of the tetrahedron, and the inner sphere touches all its sides, but is completely contained in the tetrahedron. There were just six planets, so five spaces between spheres, and there are just five regular solids...