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Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World

Euclid's geometry is well-known for its theorems concerning triangles and circles. Less popular are the contents of the tenth book, in which geometry is a means to study quantity in general. Commensurability and rational quantities are first principles, and from them are derived at least eight species of irrationals. A recently republished work by Johannes Kepler contains examples using polygons to illustrate these species. In addition, figures having these quantities in their construction form solid shapes (polyhedra) having origins though Platonic philosophy and Archimedean works. Kepler gives two additional polyhedra, and a simple means for constructing the “divine” proportion is given.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc3269
Date08 1900
CreatorsArthur, Christopher
ContributorsAnghel, Nicolae, Brozovic, Douglas, Allen, John Ed, 1937-
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsPublic, Copyright, Arthur, Christopher, Copyright is held by the author, unless otherwise noted. All rights reserved.

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