The Pythagorean Kepler

Kepler was on the cusp of the bifurcation from ancient to modern. In fact, Arthur Koestler's biography of Kepler is called The Watershed. This site is devoted to Kepler's actual watershed, and has been created by Ralph Abraham, and maintained by the Visual Math Institute.



  • Yo Who?
    Biographical information of Johannes Kepler, his life and works, with emphasis on his two Pythagorean ideas: the Solar System Model and the Music of the Spheres.
  • Kepler's Model for the Solar System, 1595
    System of spherical shells spaced by the five Platonic solids, appeared in Mysterium Cosmographicum.
  • Kepler's Music of the Spheres, 1595, 1619
    Kepler's version of the ancient Pythagorean idea of music broadcast by the crystalline spheres of the planets: pitch varies continuously with angular velocity. Appeared in Mysterium Cosmographicum, treated in detail in Harmonice Mundi.
  • Kepler's Three Laws, 1609, 1619
    The second law (equal areas) and then the first law (elliptical orbits) appeared in Astronomia Nova and the third law (period-distance relation) in Harmonice Mundi.
  • Kepler's Fibonacci/Golden Connection, 1609
    The golden ratio was known in ancient Egypt, and treated carefully in Euclid's Elements. The Fibonacci sequence appears in the work of Leonardo of Pisa, ca 1200 CE. The connection between, still mysterious today, was apparently discovered by Kepler.
  • Kepler's work on snowflakes, 1611.
    Kepler's Latin monograph, A New Years Gift, or On the six-cornered snowflake, is the first known work on morphogenesis.
  • References
    Short list of the books, articles, and websites we have consulted in creating this site.

  • Rev'd 12 apr 2003 by ralph abraham