Math 128, Modern Geometry

Math 128, Modern Geometry
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This course page is obsolete.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.

General information

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.

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/

David E. Joyce