Fall 2005, Clark University

Dept. Math. & Comp. Sci.

D Joyce

BP 322, 793-7421.

This course page is obsolete. I'll prepare a new page next time I teach the course.

- Office hours.
- Course Hours: MWF 9:00-9:50.
- Course description from Clark's Academic Catalog: Recalls Euclidean geometry and then proceeds to modern related topics: Hilbert's axioms; hyperbolic (Lobachevskian), elliptic and projective geometries, and philosophical implications of geometries without the Parallel Postulate; finite geometries; automorphism groups (Klein's Erlanger Programme). One aim is to show the beauty of deduction in mathematics. Prerequisites: high-school geometry and either a semester of college mathematics or permission.
- Course Schedule
- Textbook. We will use both
Euclid's
*Elements*, which is on line, and the textbook*Modern Geometries: Non-Euclidean, Projective, and Discrete Geometry*2nd edition, by Michael Henle. Prentice-Hall, 2001. - Syllabus
- There will be numerous short assignments, mostly from the text, occassional quizzes, two tests during the semester, and a two-hour final exam during finals week.
- The course grade will be determined from assignments and quizzes, the two midterms, and the final exam, but the precise weightings are yet to be determined.
- The following notes are in three formats: pdf for viewing, and dvi and ps for printing.

Class notes - Final exam. pdf, dvi, ps. Projective geometry.
- Desargues' theorem at http://aleph0.clarku.edu/~djoyce/java/round/desargues.html
- Notes 21. pdf, dvi, ps. Projective geometry.
- Notes 20. pdf, dvi, ps. Absolute geometry, also known as neutral geometry.
- Round triangles at http://aleph0.clarku.edu/~djoyce/java/round/round1.html
- Pappus' configuration for circles at http://aleph0.clarku.edu/~djoyce/java/round/Pappus.html
- The configuration of six circles and eight points at http://aleph0.clarku.edu/~djoyce/java/round/sixeight.html
- Notes 19. pdf, dvi, ps. Elliptic geometry. Double and single elliptic plane.
- Notes 18. pdf, dvi, ps. Distance in the hyperbolic plane.
- Notes 17. pdf, dvi, ps. Geometric analysis of the transformations of the hyperbolic plane.
- Notes 16. pdf, dvi, ps. Hyperbolic parallels, circles, horocycles, hypercycles.
- Pythagorean exposition, first draft. pdf, dvi, ps.
- Math Problem Solving Team
- Notes 15. pdf, dvi, ps. The Poincaré disk model for hyperbolic geometry.
- Notes 14. pdf, dvi, ps. Intro to hyperbolic geometry.
- Hyperbolic tilings at http://aleph0.clarku.edu/~djoyce/poincare/poincare.html
- Sample first test. pdf, dvi, ps.
- Notes 13. pdf, dvi, ps. Families of Steiner circles.
- Notes 12. pdf, dvi, ps. Further investigation into the Pythagorean theorem.
- Notes 11. pdf, dvi, ps. Circle inversion.
- Notes 10. pdf, dvi, ps. Cross ratios.
- Notes 9. pdf, dvi, ps. Introduction to Möbius geometry.
- Notes 8. pdf, dvi, ps. Further investigation into the Pythagorean theorem.
- Notes 7. pdf, dvi, ps. Transformation groups and their invariants.
- Notes 6. pdf, dvi, ps. Intro to Klein's Erlangen program.
- Notes 5. pdf, dvi, ps. Transformations, inversions, and stereographic projection.
- Compass Geometry at http://aleph0.clarku.edu/~djoyce/java/compass/
- Notes 4. pdf, dvi, ps. Introduction to plane transformations.
- Wallpaper groups of transformations at http://www.clarku.edu/~djoyce/wallpaper/
- Notes 3. pdf, dvi, ps. Construction assumptions for the proof of the Pythagorean theorem.
- Complex numbers at http://www.clarku.edu/~djoyce/complex/
- Notes 2. pdf, dvi, ps. Proofs of the Pythagorean theorem.
- The Pythagorean theorem
- Notes 1. pdf, dvi, ps. Kinds of geometries.

This page is located on the web at

http://aleph0.clarku.edu/~djoyce/ma128/