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
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
- 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
- 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
- Short list of the books, articles, and websites
we have consulted in creating this site.
Rev'd 12 apr 2003 by ralph abraham