Foundations of Geometry II

MATH 5210/7210

University of Georgia, Spring 2008

Professor Clint McCrory

Office: 402 Boyd Graduate Studies Research Center, 706-542-2576

Home: 390 Franklin Street, Athens 30606, 706-353-6517

Email: clint at math dot uga dot edu

Office hours: Monday and Wednesday 1:25-2:15, or by appointment

Class meetings

Tuesday and Thursday 11:00-12:15

Aderhold 111-113 (Math Ed computer lab)

Syllabus

The theme of the course will be three-dimensional geometry. The approach will be hands-on and problem-centered, with lots of model making. The goal is to learn geometric visualization and methods of computation in three dimensions. We'll study polyhedra: projections and slices, volume and area, solid angles, dihedral angles, decompositions, space filling, and symmetry. Special topics include Platonic solids, Archimedean solids, spherical geometry, crystal structure, and geodesic domes.

There is no required textbook or software.

Grading policy

There will be two exams and a final project. There will be no final exam. Homework will be assigned every class. (There will be short assignments Tuesday to Thursday, and longer assignments Thursday to Tuesday.) Late homework will not be accepted. Your grade will be based on the exams, project, homework, and class participation. The two exams will count 20% each, homework will count 30%, and your project will count 30%. (Class participation will be considered in borderline cases.)

Exam and project schedule

Exam 1 Thursday, February 14. Solutions.

Project proposals due Tuesday, March 4. Project ideas

Exam 2 Thursday, April 10. Comments.

Projects due Thursday, April 17.

Schedule of project presentations:

Thursday, April 17

Sherry Hix. *3D Geometry in the NCTM Standards and the Georgia Performance Standards
*Erin Mueller, Conic Sections

Amanda Bunning, Andrea McMillion, Pepper Pezold,

Christina Bartlett, Lauren Burrell, Amanda Hall, Molly McKee, Platonic Solids:

Thursday, April 24

Cristy Carr, Katie Koerten, Julie Soles,

Homework assignments

Homeworks 1-9

Homeworks 10-13

Notes and links

Cones and cylinders

Sarah's homework 2 - sections of square cylinder and cube

Lines and planes in space

Jisun's homework 3 - volume of tetrahedron and octahedron in cube

Volume relations: tetrahedron, cube, octahedron

Geometry of the icosahedron

Circumradius of the dodecahedron

Basic tetrahedron of a Platonic solid

Cauchy's proof of Euler's formula

The rhombic dodecahedron

Diamond structure

Cn and Dn symmetry classification

Jisun's project: Fractals and their application in the mathematics classroom

Felicia's project: Dodecahedron stellations

Avleen and Denna's project: 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 January 3, 2008. It was last modified on April 25, 2008.