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.

Syllabus

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

**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.