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?

General Class Information

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.

Class notes and homework are available as PDF files.  You need to have a copy of Adobe Reader to open these. 

Class Worksheets and Lecture Notes

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 – Concurrency and Triangle Centers

Chapter 5 – Collinearity and Special Triangle Points

Chapter 6 – Neutral Geometry

Chapter 7 – Introduction to Hyperbolic Geometry

Chapter 8 – Area

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

Class Lectures

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

Assignments

Assignment for January 14, 2008 — Due January 28, 2008.

Read the web page about the van Heile level’s 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 January 28, 2008 — Due February 4, 2008.

Complete Exercise Set #2.

Assignment for February 4, 2008 — Due February 11, 2008.

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

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

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

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

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

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

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

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.)

Geometry Links of Interest

·       Here is a list of quotations about mathematics and mathematicians

·       A History of Geometry from David Joyce at Clark University

·       Hyperbolic Geometry using Cabri

·       Hyperbolic Geometry using CabriJava

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Last updated 05 Oct 2011 by

David Royster david.royster@uky.edu