Experiments with Isometries
Solutions to Exercises
Solutions to Quiz F10
Isometry Lessons
Exercises for the isometry lessons.
Solutions dilatations exercises
Solutions dilatations exercises
FilecardF9.pdf
Dilatations and translations for Week 9.

Given drawings for homework for week 8
Measure this box. Copy of handout M8
Perspective index
Lesson W7 on KSEG Konstructions.
Construction thales3pts.sec
Construction perspframe3pts.sec
Class construction classW6.seg
Class construction classF5.seg
Homework solution idealDesargues.png
Solution to Quiz F4
Syllabus for Perspective
Pictures of previous perspective projects .

Filecards: accumulated responses
Practice problems
F2-MCLuses (in class)
F2-kseg Lab (in class)
nicer Exercises
Advice on how-to do things
Affine Geometry Index
Classcomm-firstaid
netMA403
calendar
Syllabus for Affine
access Classcomm
download texPad
access texWins

Fall 2009 Course Description:

MATH 403: COLLEGE GEOMETRY

This junior/senior level course in classical Euclidean geometry from a contemporary viewpoint is woven from five threads (themes)
1. The Physical Origins of Greek Geometry.
2. Renaissance Perspective and 3-dimensional Drawing.
3. The Industrial Origins of Cartesian Geometry.
4. Klein's Erlangen Program to Unify Geometry.
5. The Geometry in Computer Graphics.

The initial 3 week unit on affine Geometry, including the theorems of Ceva, Menelaus, Desargues and Pappus (Tondeur, Ch1) is a good review of Euclidean plane geometry using vector methods. There follows a 4-week unit on the practice and theory of perspective drawing (Francis, Ch3) which serves as an introduction to visualizing 3-dimensions and to classical projective geometry. A 2 week unit on dilatations (parts of Tondeur, Ch2), applied to constructing Euler's line and the Nine-point circle, introduces transformational geometry. Klein's Erlangen Program, defining geometries in terms of their isometry groups, and the classification of isometries (congruences) in the Euclidean plane occupies remaining 6 weeks of the course.

There will be weekly graded assignments, including homework submitted online. The date of the midterm (written hourly) will be Friday, 10oct09. There is a takehome exam due 20nov09 The semester project is due on 4dec09, and the 3 hr written final is at 8am on 18dec09. Please resolve conflicts early in the semester and do not schedule absences on announced test dates. The course grade assesses the student's final comprehension and achievement in the course. The traditional average is 3.2 based a weighten average (30% final, 15% project, 15% midterm, and 40% weekly work, including class participation.)

The unit on perspective will include a substantial visual project, such as a drawing, model construction, computer animation, video etc. The form and content of this project is open to negotiation, and it is adapted to the interest and skill of the student. The project requires a proposal, progress report and 4-6 pages of written documentation in LaTeX. Drafts of this documentation will be returned for correction.

This course satisfies requirements in several math and education curricula, but can also be taken as a technical elective in science and engineering. Its strong emphasis on visual comprehension and its historical flavor makes it accessible to students in the fine and applied arts. The course may be taken for 3 or 4 credit hours. The 3 credit version does not require the the project on perspective and its documentation.

The prerequisites for the course are Calculus III (MA241 or its equivalent) for the use of vectors, and MA347 or its equivalent for the maturity in understanding and writing rigorous proofs gained there. Consent of the instructor may be obtained on the basis of some other, substantial experience with mathematical proofs.

Students are encouraged to participate in mathematically meaningful activities such as seminars, films, exhibits, cultural events etc. Reports on such activities may be used to make up missed assignments.

Feel free to use the following Google Custom Search Element to surf this site. But please note, your search will find items written by students and collaborators. Please respect their intellectual property, and write me if you find any pages that should not be visible.