Pick up your portfolios between 11-noon M16.
Check calendar for walk-in office hours.
Pick up your portfolios between 11-noon M16.
Check calendar for walk-in office hours.
There is a correction on the takehome in the notes.
See the revised syllabus for current homework problems.
Pictures of perspective projects .
An important note on homework W11
This course satisfies requirements in several math and education curricula, but can also be taken as a technical elective in science and engineering. It's strong emphasis on visual comprehension and its historical flavor makes it accessible to students in the fine and applied arts.
The senior level lecture/project course is held together by five
interwoven threads or themes of traditional
interest in classical Euclidean geometry from a contemporary
viewpoint, in space as well as in the plane.
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.
A brief review of Euclidean plane geometry (high-school) is followed by a 2-week unit on affine geometry using vector methods (freshman-calculus) culminating in Desargues' theorem in the plane. There follows a 3-week unit on the history and geometry of perspective drawing. This serves as an introduction to visualizing 3-dimensions and to classical projective geometry. Klein's Erlangen Program to defining geometries in terms of their isometry groups, and the classification of isometries (congruences) in the Euclidean plane and 3-space will occupy a major portion of the semester. The unit on Euclidean motions of 3-space, including a introduction to quaternions and the orthogonal group, rounds out the semester.
There will be weekly graded assignments, including homework and quizzes. The date of the midterm (written hourly) will be Friday, 28sep07. The written final is scheduled for 8am, Wednesday, 12dec07. 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 on 30% final, 15% project, 15% midterm, and 40% weight on weekly work.
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 written documentation, including a proposal and a bibliography. Drafts of this documentation will be returned for correction.
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.