Math 104: Fundamental Problems of Geometry
Emily Dumas
Brown University
Spring 2006

A tiling of the hyperbolic plane by ideal quadrilaterals. All of the stick figures are congruent. (Image produced by David Wright.)

General Information

Text	Euclidean & Non-Euclidean Geometries: Development and History, Third Edition, by Marvin Jay Greenberg ISBN 0716724464 (+ supplementary readings from other texts as needed)
Instructor	Emily Dumas
Office	Kassar House 114
Phone	401-863-7957
Email
Office Hours	Tues 12:00-1:00pm, Wed 2:00-3:00pm, and by appointment
Meeting Time	Tues and Thurs 10:30 - 11:50am (I hour)
Location	Barus & Holley 157
Homework Policies	Problem assignments will be given approximately once a week, with due dates announced at the time of assignment (usually one week later). Homework must be turned in at the start of lecture on the due date.
	Late homework will NOT be accepted. There are no exceptions to this policy.

Homework and Reading

2006-01-26 - Chapter 1 of Greenberg
2006-01-31 - Chapter 2 of Greenberg
2006-01-31 - Homework 1 due on Tuesday, February 7
2006-02-02 - Betweenness from Chapter 3 of Greenberg (pp. 70-82)
2006-02-07 - Congruence from Chapter 3 of Greenberg (pp. 82-92)
2006-02-07 - Homework 2 due on Tuesday, February 14
2006-02-09 - Continuity and Parallelism from Chapter 3 of Greenberg (pp. 93-102)
2006-02-14 - Chapter 4 of Greenberg
2006-02-14 - Homework 3 due on Thursday, February 23
2006-02-28 - Chapters 6 and 7 of Greenberg
2006-02-28 - Homework 4 due on Tuesday, March 7
2006-03-07 - Homework 5 due on Tuesday, March 14
2006-03-14 - Chapter 9 of Greenberg
2006-03-14 - Homework 6 due on Tuesday, March 21
2006-03-23 - Homework 7 due on Thursday, April 6
2006-04-04 - Chapter 10 of Greenberg
2006-04-06 - Homework 8 due on Thursday, April 13
2006-04-11 - Supplementary reading (recommended, not required): Hyperbolic Geometry by Cannon, Floyd, Kenyon, and Parry; from Flavors of Geometry, MSRI Publications, volume 31
2006-04-13 - Homework 9 due on Thursday, April 20
2006-04-20 - Homework 10 due on Thursday, April 27
2006-04-27 - Homework 11 due on Thursday, May 4

Grading

Your final grade will be determined by your homework scores, two in-class quizzes, and a cumulative final exam. The take-home final exam will be distributed during reading period and will be due during the final exam period. These factors will be weighted as follows:

Homework	Weekly	20%
Quiz 1	Thursday, February 23	15%
Quiz 2	Thursday, March 23	15%
Final Exam (take-home)	Assigned: Friday, May 5, Noon EDT Due: Friday, May 12, 4:00pm EDT	50%

Reserve List

The following items are on reserve in the Sciences Library:

Euclidean and Non-Euclidean Geometries: Development and History, 3rd ed, by Marvin Jay Greenberg. (Main textbook)
The Thirteen Books of Euclid's Elements, Edited and translated by T. L. Heath. (Supplementary reference)
Geometry: Plane and Fancy by David A. Singer (Supplementary reference)
Introduction to hyperbolic geometry by Arlan Ramsay (Supplementary reference)

Geometry Resources

Euclidean Geometry
- Euclid's Elements Online, adapted by David Joyce of Clark University.
  Geometric constructions from the Elements are presented here as interactive Java applets.
- Oliver Byrne's 1847 Edition of the Elements from the UBC Digital Mathematics Archive.
  Presented as scanned images of the pages. This edition is unique in its use of beautiful colored diagrams in place of letters and symbols where possible.
- Geometry Applets from cut-the-knot.org.
  An huge collection of interactive constructions, including:
  - 54 proofs of the pythagorean theorem
  - Pappus' Theorem
Hyperbolic Geometry
- From the (now-defunct) Geometry Center:
  - Models of the Hyperbolic plane, including Minkowski, Poincare, Klein
  - Movie of the Klein-Poincare isomorphism (and other other isomorphisms)
- Hyperbolic geometry links from the Geometry Junkyard (includes both 2- and 3-dimensional hyperbolic geometry).
- Pairs of corresponding figures in the Klein and Poincare models from Visualization of the Lobachevskian Plane at the University of Belgrade
- Klein-Poincare isomorphism diagrams by mathematical hobbyist Tadao Ito

Math 104: Fundamental Problems of Geometry Emily Dumas Brown University Spring 2006