David 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.) |

Text |
Euclidean & Non-Euclidean Geometries: Development and History, Third Edition, by Marvin Jay Greenberg ISBN 0716724464 (+ supplementary readings from other texts as needed) |
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Instructor | David Dumas |

Office | Kassar House 114 |

Phone | 401-863-7957 |

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. |

**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

Homework | Weekly | 20% |
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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% |

- 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)

**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:

**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

- From the (now-defunct) Geometry Center: