## Math 329, Geometry, Spring 2011

M 4:40 - 6:20 1S-107 (Section 6952)

W 4:40 - 6:20 1S-219 (Section 6952)

Instructor: |
Joseph Maher |

Office: |
1S-222 |

Office hours: |
M 2:30-4:30, W 3:30-4:30 |

Webpage: |
http://www.math.csi.cuny.edu/~maher/teaching |

Email: |
joseph.maher@csi.cuny.edu |

Phone: |
(718) 982-3623 |

**Required textbook:** The Four Pillars of Geometry by John Stillwell. You must also buy an (inexpensive) compass and ruler.

**Recommended additional textbook:** The Shape of Space, Second Edition, by Jeff Weeks.

**Goals:** The primary goal of this course is to understand geometry from different viewpoints, both classical and modern. Another goal is to learn how to write concise but complete arguments.

**Homework:** Assignments will be announced in class, sometimes referring to this website. *I highly recommend working jointly on homework problems with fellow students.* You are expected to be familiar with high-school geometry; for review, see www.mathopenref.com, a free online math textbook for high-school geometry.

**Grading:** The course grade will be determined as follows: 10% Homework and quizzes, 25% Exam 1, 25% Exam 2, 40% Final Exam.

**Help:** My office hours are on Mondays 2:30-4:30pm and Wednesdays 3:30-4:30pm, in my office, 1S-222.

**Optimal Method of Study:** (1.) Come to class (attendance is mandatory). (2.) Read the relevant sections and websites after class. (3.) Do the homework. Leave time to think--do not put homework off until it is due! (4.) Compare your solutions with other students. (5.) Come to office hours with any questions.

Important Dates (http://www.csi.cuny.edu/currentstudents/academiccalendars/)

Date | Topic | Reading | Homework |
---|---|---|---|

Mon Jan 31 | Euclidean constructions | 1.1 - 1.3 | 1.2.1-1.2.3, 1.3.3-1.3.6 |

Wed Feb 2 | Thales' Theorem, similar triangles | 1.4 - 1.5 | 1.4.1-1.4.4 |

Mon Feb 7 | Parallel and congruence axioms | 2.1 - 2.2, properties of quadrilaterals | 2.1.1-2.1.5, 2.2.1-2.2.3 |

Wed Feb 9 | Pythagorean Theorem | 2.3 - 2.5, pythagorean triples | 2.3.2-2.3.3, 2.4.1, 2.4.4, 2.5.1-2.5.5 |

Mon Feb 14 | Proof of Thales' Theorem, angles in a circle | 2.6 - 2.7, another construction for squaring a rectangle | 2.6.1, 2.7.1-2.7.5 |

Wed Feb 16 | Pythagorean Theorem revisited, other proofs | 2.8, cut-the-knot, gogeometry, Givental | 2.8.1-2.8.3 |

Mon Feb 21 | No class |
||

Wed Feb 23 | Coordinates | 3.1 - 3.5 | 3.2.1-3.2.6, 3.3.1, 3.4.1-3.4.3 |

Mon Feb 28 | Concurrence in triangles, chords arcs and angles in a circle | regentsprep and mathopenref | Regents Exam |

Wed Mar 2 | Geometry on NY Regents Exam | regentsprep and mathopenref | |

Mon Mar 7 | Review | ||

Wed Mar 9 | Exam 1 |
||

Mon Mar 14 | Isometries, Three Reflections Theorem | 3.6 - 3.8 | 3.6.1-3.6.4, 3.7.1-3.7.3 |

Wed Mar 16 | Classification of plane isometries, group of isometries | cut-the-knot, wikipedia, 7.1 | 7.1.1-7.1.3 |

Mon Mar 21 | Vectors | 4.1 - 4.2 | 4.1.3-4.1.4, 4.2.1-4.2.2 |

Wed Mar 23 | Concurrence, inner product | 4.3 - 4.6, cut-the-knot | 4.3.2-4.3.5, 4.4.1-4.4.2, 4.5.1-4.5.3 |

Mon Mar 28 | Matrices, transformations, isometries | 4.7, 7.2 | 7.2.1-7.2.6 |

Wed Mar 30 | Spherical geometry | 7.4 - 7.5, Polking, Strogatz (NYT article) | 7.4.1-7.4.5 |

Mon Apr 4 | Spherical triangles and Girard's Theorem | Shape of Space 9, Polking | Dimensions Lectures 1 and 9 |

Wed Apr 6 | Review | ||

Mon Apr 11 | Exam 2 |
||

Wed Apr 13 | Perspective drawing, projective plane, Desargues Theorem | 5.1 - 5.3, 6.1 - 6.2 | 5.1.1-5.1.3, 5.2.2, 5.3.1-5.3.2 |

Mon Apr 18 | Spring break |
||

Wed Apr 20 | Spring break |
||

Mon Apr 25 | Spring break |
||

Wed Apr 27 | Hyperbolic geometry introduction | 8.1 - 8.9, Shape of Space 10, 15, Isometries of the hyperbolic plane | Escher's hyperbolic plane, cut-the-knot1, cut-the-knot2 |

Mon May 2 | Euler's formula and regular polyhedra | Regular polyhedra classified using the Euler Characteristic | Euler's formula (AMS feature column) |

Wed May 4 | Classification of surfaces | Shape of Space 1 - 6, 8, and Fiedorow | Online resources for Shape of Space |

Mon May 9 | Geometry on surfaces | Shape of Space 7, 11 | |

Wed May 11 | Gauss-Bonnet Theorem and Euler Characteristic | Shape of Space 12 | |

Mon May 16 | Review | ||

Wed May 18 | Review | ||

Mon May 23 | Final |

**Related links:**

Excellent links about geometry: Cut the knot and Geometry Junkyard.

Euclidean geometry, compass and straightedge constructions: Euclid's Elements online, constructible regular polygons (scroll down).

From an excellent website on the history of mathematics, the three famous unsolved problems of Greek mathematics: Doubling the cube, squaring the circle, trisecting an arbitrary angle.

Construction of a regular pentagon in given circle (shown with a nice applet). A related link is Approximate Construction of Regular Polygons: Two Renaissance Artists.

These are the notes I make for class, they are probably not of much use to anyone else.