## 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.

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

Midterm 1 solutions

Sample midterm 2

Sample midterm 2 solutions

Midterm 2 solutions

Sample final

Sample final solutions

Final solutions