MATH 6118 090

Non-Euclidean Geometry

SPRING 2008

Dr. David C. Royster

`david.royster@uky.edu`

Thought for the
Day:* **
If toast always lands butter-side down and cats always land on their feet,
what happens when you strap a piece of toast on the back of a cat?*

Class Syllabus . Click here
for a PDF version for printing.

List of topics to be covered each day. Click here for a
PDF version for printing.

Chapter 1 *The Origins and Weapons of Geometry
Read this short story about π*

Chapter 2 *The Rules of the Game *

Chapter 3 *Euclidean Geometry - Axiom Systems and Review of Results*

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter
9 *Poincarι Disk Model of the Hyperbolic
Plane*

Chapter
10 *Poincarι Half-Plane Model of the Hyperbolic Plane*

Chapter
11
*Horocycles and Hypercycles*

Chapter 12 *Hyperbolic Trigonometry*

Chapter 13 *Analytic Hyperbolic Geometry*

These are the PowerPoint presentations used in class, saved in two formats. Both are PDF files (to insure font fidelity). Slides are the slides themselves in color and Notes are the slides 3 to a page in grayscale.

Lecture 2 Triangle Centers and Ceva's Theorem | Slides | Handouts |

Lecture 3 More triangle centers and Collinearity | Slides | Handouts |

Lecture 4 Neutral Geometry | Slides | Handouts |

Assignment for

Read the
web page about the van Heile levels of geometric
understanding and read either the Fuys, ** et al**., or the Malloy and Friel
article.

Read the articles on the web page about definitions. Be prepared to discuss the concept of definition.

Complete Exercise Set #1. (Available as PDF file.)

Assignment for

Complete Exercise Set #2.

Assignment for

Complete
Exercise Set #3. (Available as a
PDF file.)

Assignment for February 11,
2008 Due February 25, 2008.

Complete
Exercise Set #4. (Available as a
PDF file.)

Assignment for February 25, 2008
Due March 10, 2008.

Complete
Exercise Set #5. (Available as a
PDF file.)

Assignment for March 10, 2008
Due March 17, 2008.

Complete
Exercise Set #6. (Available as a
PDF file.)

Assignment for April 14, 2008
Due April 21, 2008.

Complete
Exercise Set #7. (Available as a
PDF file.)

Assignment for April 21, 2008
Due April 28, 2008.

Complete
Exercise Set #8. (Available as a
PDF file.)

·
Here is a list of quotations
about
mathematics and mathematicians

·
A History of
Geometry from David Joyce at

·
Hyperbolic
Geometry using Cabri

·
Hyperbolic
Geometry using CabriJava

Back to the My Home Page

Last updated 05 Oct 2011 by

David Royster david.royster@uky.edu