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

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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 ... continued below

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Arthur, Christopher August 2002.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 831 times , with 7 in the last month . More information about this thesis can be viewed below.

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  • Arthur, Christopher

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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.

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  • August 2002

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  • Sept. 26, 2007, 2:36 a.m.

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  • Aug. 13, 2013, 4:22 p.m.

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Arthur, Christopher. Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World, thesis, August 2002; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc3269/: accessed June 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .