Department of Mathematics, College of Staten Island, City University of New York (CUNY)

Geometry MTH 329 Section 17910 Spring 2014

Monday & Wednesday, 2:30 pm - 4:25 pm, Room 1S-218

Prof. Ilya Kofman

Office:   1S-209   phone: (718) 982-3615

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.

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.

Homework: Assignments will be announced in class, sometimes referring to this website. It is very important to do the homework to understand the topics covered in the class. I highly recommend working jointly on homework problems with fellow students. You are expected to be familiar with high-school geometry; for review, see, a free online math textbook for high-school geometry.

Exams: We will have two exams during the semester on Wednesday, March 5 and on Wednesday, April 9, and you must take the final exam at the time scheduled by the college.

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 and Wednesdays 1:00pm - 2:15pm, in my office, 1S-209. Email is the fastest way to contact me.

How to 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 or email with any questions. (6.) To study for a math exam, you must DO MORE PROBLEMS from past exams and textbook.

Schedule of lectures and homework:

Section and problem numbers generally refer to The Four Pillars of Geometry by John Stillwell.

Date Topic Reading Homework
Mon Jan 27   Euclidean constructions 1.1 - 1.3 1.2.1-1.2.3, 1.3.3-1.3.6
Wed Jan 29   Thales' Theorem, similar triangles 1.4 - 1.5 1.4.1-1.4.4
Mon Feb 3   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 5   Pythagorean Theorem 2.3 - 2.5 2.3.2-2.3.3, 2.4.1, 2.4.4, 2.5.1-2.5.5
Mon Feb 10   Proof of Thales' Theorem, angles in a circle 2.6 - 2.7, Squaring a rectangle, Regular pentagon 2.6.1, 2.7.1-2.7.5
Wed Feb 19   Pythagorean Theorem revisited, other proofs 2.8, cut-the-knot, gogeometry, Givental 2.8.1-2.8.3
Thurs Feb 20   Coordinates 3.1 - 3.5 3.2.1-3.2.6, 3.3.1, 3.4.1-3.4.3, Special Homework 1
Mon Feb 24   Concurrence in triangles, chords arcs and angles in a circle regentsprep, mathopenref NYS Regents Exams
Wed Feb 26 Geometry on NY Regents Exam regentsprep, mathopenref Practice Regents Exams
Mon Mar 3   Review for Exam 1 Old Exams
Wed Mar 5   Exam 1
Mon Mar 10   Isometries, Three Reflections Theorem 3.6 - 3.8, Applet (Java version) 3.6.1-3.6.4, 3.7.1-3.7.3
Wed Mar 12   Classification of plane isometries, group of isometries 7.1, cut-the-knot, wikipedia 7.1.1-7.1.3
Mon Mar 17   Vectors 4.1 - 4.2 4.1.3-4.1.4, 4.2.1-4.2.2
Wed Mar 19   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 24   Linear transformations and matrices, complex numbers 4.7, 7.2 4.7.1-4.7.5, 7.2.1-7.2.6
Wed Mar 26   Spherical geometry 7.4, Dimensions ch 1 and 9, Strogatz (NYT) 7.4.1-7.4.5
Mon Mar 31   Spherical triangles and Girard's Theorem Shape of Space ch 9, Polking , Great circle map Girard's Theorem (slides)
Wed Apr 2   Spherical rotations, Euler's formula 7.5, Polking , EscherMath Gall-Peters (West Wing), Gall-Peters (wikipedia)
Mon Apr 7   Review for Exam 2 Old Exams
Wed Apr 9   Exam 2
Wed Apr 23   Perspective drawing, projective plane 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 28   Taxicab geometry Taxi! (AMS feature column)
Wed Apr 30   Hyperbolic geometry 8.1 - 8.9, Shape of Space ch 10, Jos Leys, Isometries of hyperbolic plane, cut-the-knot-1
cut-the-knot-2, Escher's hyperbolic plane
8.1.1 - 8.1.4, 8.2.1 - 8.2.3, 8.4.1, 8.6.1 - 8.6.6, Special Homework 2
Mon May 5   Euler's formula and regular polyhedra Regular polyhedra (cut-the-knot) and slides Euler's formula (AMS feature column), Dimensions ch 2 - 4
Wed May 7   Classification of surfaces Shape of Space 1 - 6, 8, and Fiedorow Online resources for Shape of Space
Mon May 12   Geometry on surfaces, Gauss-Bonnet Theorem Shape of Space ch 11-12, Givental
Wed May 14   Review for final exam Old Exams
Mon May 19   Final Exam 2:30 - 4:25pm in room 1S-218

Online Resources and related links:

Disability policy: Qualified students with disabilities will be provided reasonable academic accommodations if determined eligible by the Office for Disability Services. Prior to granting disability accommodations in this course, the instructor must receive written verification of student's eligibility from the Office of Disability Services, which is located in 1P-101. It is the student's responsibility to initiate contact with the Office for Disability Services staff and to follow the established procedures for having the accommodation notice sent to the instructor.

Integrity policy: CUNY's Academic Integrity Policy is available online at