Foundations of Geometry II
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
Tuesday and Thursday 11:00-12:15
Aderhold 111-113 (Math Ed computer lab)
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.
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, Geometry in Architecture
Tuesday, April 22
Christina Bartlett, Lauren Burrell, Amanda Hall, Molly McKee, Platonic Solids: Extreme Truncations and Duality
Nicholas Cluster, Colleen Garrett, Ron Panapoi, Dana TeCroney, Stellations
Karina Brown, Dual Archimedean Solids
Thursday, April 24
Cristy Carr, Katie Koerten, Julie Soles, 3D Puzzles
Sharon O'Kelley, Kaleidocycles
Ryan Fox, Euler's formula
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
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.