| 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: 132
Past 30 days: 4
Yesterday: 0
|
| Creator (Author): |
|
|
|---|---|---|
| Publisher Info: |
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
|
|
| Original Creation Date: | August 2002 | |
| 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: |
Name:
Master of Arts
Level:
Master's
Discipline:
Mathematics
Department:
Department of Mathematics
Grantor:
University of North Texas
|
|
| Language(s): | ||
| Subject(s): |
|
|
| Keyword(s): | La Grange | manifold | binary operations | |
| Contributor(s): |
|
|
| Partner: |
UNT Libraries
|
|
| Collection: |
UNT Theses and Dissertations
|
|
| Identifier: |
|
|
| 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.
|
|
