This semester based (16 week) 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, and Desargues, 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 which serves as an introduction to visualizing 3-dimensions and to classical projective geometry. A 2 week unit on dilatations 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.
This course satisfies requirements in several math and education curricula, in particular the Illinois Certification Testing System, Field 115: Mathematics, November 2003. The course 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 project on perspective and its documentation.
The student will also learn LaTeX for the preparation of mathematical documents (software is provided) and KSEG (software can be downloaded free) for the preparation of mathematical figures.
Prospective students need to consult with the instructor for permission to take the course. For University of Illinois students, the prerequisites are met by those portions of Calculus III (MA241) that introduces and uses vectors, and MA347 for the maturity in understanding and writing proofs. If you wish to be absolutely certain that you are well prepared to take the course, check here.