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

PDF Version Also Available for Download.

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 ... continued below

Creation Information

Arthur, Christopher August 2002.

Context

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 797 times , with 14 in the last month . More information about this thesis can be viewed below.

Who

People and organizations associated with either the creation of this thesis or its content.

Chair

Committee Members

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Arthur, Christopher

Provided By

UNT Libraries

Library facilities at the University of North Texas function as the nerve center for teaching and academic research. In addition to a major collection of electronic journals, books and databases, five campus facilities house just under six million cataloged holdings, including books, periodicals, maps, documents, microforms, audiovisual materials, music scores, full-text journals and books. A branch library is located at the University of North Texas Dallas Campus.

Contact Us

What

Descriptive information to help identify this thesis. Follow the links below to find similar items on the Digital Library.

Degree Information

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.

Subjects

Language

Identifier

Unique identifying numbers for this thesis in the Digital Library or other systems.

Collections

This thesis is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. __Some ETDs in this collection are restricted to use by the UNT community__.

What responsibilities do I have when using this thesis?

When

Dates and time periods associated with this thesis.

Creation Date

  • August 2002

Added to The UNT Digital Library

  • Sept. 26, 2007, 2:36 a.m.

Description Last Updated

  • Aug. 13, 2013, 4:22 p.m.

Usage Statistics

When was this thesis last used?

Yesterday: 0
Past 30 days: 14
Total Uses: 797

Interact With This Thesis

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

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 February 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .