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

Description:

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.

Creator(s): Arthur, Christopher
Creation Date: August 2002
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
Usage:
Total Uses: 323
Past 30 days: 5
Yesterday: 1
Creator (Author):
Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: August 2002
  • Digitized: July 13, 2007
Description:

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.

Degree:
Level: Master's
Discipline: Mathematics
Language(s):
Subject(s):
Keyword(s): La Grange | manifold | binary operations
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 50444717 |
  • ARK: ark:/67531/metadc3269
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
License: Copyright
Holder: Arthur, Christopher
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.