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Professor: George Francis

Contact: gfrancis@illinois.edu, Office: 101 Altgeld Hall

Textbook: "Vectors and Transformations" by Ph. Tondeur, Publish or Perish, 1993.

Online Lecture Notes, Geogebra and GEX2.0 geometry software (free)

This junior/senior level course on 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 core unit (Tondeur Ch.1) is on affine geometry, including the theorems of Ceva, Menelaus, and Desargues. This is a good review of Euclidean plane geometry using vector methods. There follows a short transition (part of Tondeur Ch. 2 and 3), including dilatations as applied to constructing Euler's Line and the Nine-Point Circle to transformational geometry.

The second core unit of the course is on the practice and theory of perspective drawing which serves as an introduction to visualizing 3-dimensions and to classical projective geometry.

The third core unit (Tondeur Ch. 4) is on Klein's Erlangen Program, defining geometries in terms of their isometry groups, and the classification of isometries (congruences) in the Euclidean plane.

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 GEX2.0 (software can be downloaded free) for the preparation of mathematical figures.

Prerequisites for this course is MA241 and MA347 or the equivalent. The latter requires permission by the instructor to take the course. The final is on Thursday, 18dec14 at 7:00-10:00 pm. This course is not required to offer a conflict final, so resolve all conflicts early. Do not schedule travel before the final. The course grade is base on 30% for the final, 10% for each of the tests, and 30% for class participation.