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.

Grantor dc:publisher

University of North Texas

Year dc:date

2002

Author dc:creator

• Arthur, Christopher

Contributors dc:contributor

• Anghel, Nicolae
• Brozovic, Douglas
• Allen, John Ed, 1937-

• Kepler, Johannes, 1571-1630. Harmonices mundi.
• Geometry.
• Book X
• commensurability
• La Grange
• manifold
• binary operations

Statement dc:rights

• Public
• Copyright
• Arthur, Christopher
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 50444717
https://digital.library.unt.edu/ark:/67531/metadc3269/
ark: ark:/67531/metadc3269

OAI identifier oai:identifier

info:ark/67531/metadc3269