Foundations of Geometry I
MATH 5200/7200
University of Georgia, Fall 2008

Professor Clint McCrory
Office: 402 Boyd Graduate Studies Research Center, 706-542-2576
Home: 390 Franklin St., Athens 30606, 706-353-6517
Email: clint at math dot uga dot edu

Class meetings
Monday-Wednesday-Friday 11:15-12:05
Aderhold 111-113 (Math Ed computer lab)

Office hours
Monday - Friday 12:30-2:00
or by appointment.

Textbook and software
There is no textbook for this course. The software Geometer's Sketchpad (Student Edition) is required. It is available from the University Bookstore (bundled with the statistics software Fathom for $49.95). It can also be ordered from Key Curriculum Press.

The course has three parts:
A. Geometer's Sketchpad: constructions and proofs
B. Axioms and basic theorems of plane geometry
C. Trigonometry and non-Euclidean geometry

Schedule of topics (revised 10/25)

Exams, homework, and grading
There will be three in-class exams, a final project, and a final exam. The first exam will also have a take-home part. Homework will be assigned almost every class. Your grade will be based on the exams, project, homework, and class participation. The three exams will count 15% each, homework will count 20%, the project will count 15%, and the final exam will count 20%. Class participation will be considered in borderline cases.

Homeworks 1-7
Homeworks 8-13
Practice problems
Homeworks 14-19

Exam 1: Friday, September 19 (take-home part due Monday, September 22). Exam 1A, Exam 1A Solutions, Exam 1B, Exam 1B Solutions.
Project proposals due: Friday, October 10. Project suggestions
Exam 2: Wednesday, October 22. Solutions.
Exam 3: Wednesday, December 3. Solutions.
Projects due: Friday, December 5
Review session: Wednesday, December 10, 1:00-2:30 pm (Aderhold 111
Final Exam: Friday, December 12, 12:00-3:00 pm

Notes from class
A. Geometer's Sketchpad: constructions and proofs
August 18, August 20, August 22 (GSP sketch) - Michelle Chung
Arc angle theorem

Pythagorean Theorem: Mary Catherine Clark, Jenny Whitt, Adam Brown, Eunmi Cho
Similar triangles
Greek constructions
Constructions and proofs

August 25, 27, 29 - Eric Gold

Presentations September 3: Laura Hill, Russ Ivey, Charnelle Davenport
September 3, 5 - Allyson Hallman

Schedule for September 8, 10, 12
Presentations September 8:
Laura Lowe's group
Becky Mohl's group, part 1, part 2, Charnelle's version
Presentations September 10:
Laura Singletary's group part1, part 2
Michelle Chung's group
Presentations September 12:
Eric Gold's group
Allyson Hallman's group
Comments on the presentations

B. Axioms and basic theorems of plane geometry
Axioms for plane geometry
Basic theorems
Definitions involving circles

September 22, 24, 26 - Becky Mohl
Presentations September 26: Laura Hill, Kim Newman, Julia Wilson

September 29 - Laura Singletary
Presentations September 29: Amanda Newton, Lindy Wallace, Jenny Whitt

Proofs of the basic theorems (homework 11)
Group A: Isosceles triangles, Parallels
Group B: Congruence
Group C: Area, Similarity
October 6, 8, 10 - Michelle Chung

Side-Angle-Side Similarity
Straight Angle Theorem
Useful theorems
October 13, 15, 17 - Eric Gold

C. Trigonometry and non-Euclidean geometry
Definition of sine and cosine
Trig addition formulas
Presentations October 27: Lindy Wallace, Laura Hill, Mary Catherine Clark
October 24, 27, 29 - Allyson Hallman

Presentations November 3: Jenny Whitt, Becky Mohl
November 3, 5, 7 - Laura Lowe

November 10, 11, 12, part a, part b, part c, part d - Becky Mohl

Axioms and basic theorems for spherical geometry
November 17, November 19, November 21 - Laura Singletary

Review for exam 3

Schedule of project presentations
Friday, December 5
(1) Taxicab Geometry - Adam Brown, Kim Newman, Lindy Wallace, Jenny Whitt
(2) Fibonacci Numbers - Mary Catherine Clark
Monday, December 8
(1) Napoleon's Theorem - Eunmi Cho, Mandy Shealy, Amelia Slaughter, Julie Wilson. GSP files
(2) Egyptian Geometry- Rachel Bonilla, Charnelle Davenport, Glen Gibbs, Whitney Wright
Tuesday, December 9
Paper Folding - Eric Gold and Becky Mohl. GSP files

Useful links and references
Schaum's Outline of Geometry - good reference, helpful for review
The Math Forum - wonderful resource for teachers
Euclid's Elements - web version by David Joyce of Clark University
Geometry from the Land of the Incas - amazing animations
Trigonometric Delights, by Eli Maor - fascinating history
Geometer's Sketchpad Advanced Sketch Gallery - many useful GSP toolkits
Hyperbolic GSP
- user's guide for Judit Abardia Bochaca's software
The Poincare Half-Plane, by Saul Stahl - excellent undergraduate textbook
Lenart Sphere - hands-on tool for studying spherical geometry

All academic work must meet the standards contained in the document A Culture of Honesty. Students are responsible for informing themselves about those standards before performing any academic work.

This page was created on August 1, 2008. It was last revised on December 17, 2008.