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Mathematical Treasure: Kepler's Harmonices mundi

Frank J. Swetz (Pennsylvania State University)

Johann Kepler's (1571-1630) search for order in the universe led to his arrangement of the five Platonic Solids as a divine plan for the movement of the planets, a theory which he first articulated in his Mysterium Cosmographicum (1596). In 1619, he provided further explanation and refinement in his Harmonices mundi [Harmony of the Worlds]. The Harmony consisted of five books in which Kepler explored regular polyhedra further, gave the first systematic treatment of tessellations, provided a proof of the existence of only thirteen convex uniform polyhedra, and stated his third law of planetary motion. Images of several pages from this book follow.

The images above are presented courtesy of the History of Science Collections, University of Oklahoma Libraries.

For more images from Kepler's Harmonices mundi, see Mathematical Treasure: Kepler's Harmony of the Worlds.

Index to Mathematical Treasures

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Kepler's Harmonices mundi," Convergence (May 2019)