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

Geometry MTH 329 Spring 2017

Monday & Wednesday, 2:30 pm - 4:25 pm, Room 1S-116

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 proofs that are both concise and complete.

Required textbook: The Four Pillars of Geometry by John Stillwell (ISBN-13: 978-0387255309). You must also buy an (inexpensive) compass and ruler.

Recommended additional textbook: The Shape of Space, Second Edition, by Jeff Weeks (ISBN-13: 978-0824707095).

Homework: Assignments will be announced in class, usually 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, a free online math textbook for high-school geometry.

Exams: There will be two in-class exams: Exam 1 on Wednesday, March 8 and Exam 2 on Wednesday, April 5. Without exception, you must pass the exams to pass this course, and you must take the final exam at the time scheduled by the college.

Grading: The course grade will be determined by your scores on homework, quizzes, exams and final exam.

Help: My office hours are on Mondays 12:00pm - 2:30pm, 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.) Come to office hours or email with any questions. (5.) To study for a math exam, you must DO MORE PROBLEMS from past exams and textbooks.

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 30   Euclidean constructions 1.1 - 1.3 1.2.1-1.2.3, 1.3.3-1.3.6
Wed Feb 1   Thales' Theorem, similar triangles 1.4 - 1.5, cut-the-knot 1.4.1-1.4.4
Mon Feb 6   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 8   Pythagorean Theorem 2.3 - 2.5 2.3.2-2.3.3, 2.4.1, 2.4.4, 2.5.1-2.5.5
Wed Feb 15   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 22   Pythagorean Theorem revisited, other proofs 2.8, cut-the-knot, gogeometry, Givental 2.8.1-2.8.3
Mon Feb 27   Coordinates 3.1 - 3.5 3.2.1-3.2.6, 3.3.1, 3.4.1-3.4.3, Special Homework 1
Wed Mar 1   Concurrence in triangles, chords arcs and angles in a circle mathopenref NY Regents geometry exams
Mon Mar 6 Vectors 4.1 - 4.2 4.1.3-4.1.4, 4.2.1-4.2.2
Wed Mar 8   Exam 1 Exam 1 from Spring 2014
Mon Mar 13   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
Wed Mar 15   Isometries, Three Reflections Theorem 3.6 - 3.8, Applet (Java version) 3.6.1-3.6.4, 3.7.1-3.7.3
Mon Mar 20   Classification of plane isometries, group of isometries 7.1, cut-the-knot, wikipedia, glide reflections 7.1.1-7.1.3
Wed Mar 22   Spherical geometry: points, lines and incidence Ryan, Harvard Dimensions ch 1 and 9, Strogatz (NYT)
Mon Mar 27   Spherical geometry 7.4 7.4.1-7.4.5
Wed Mar 29   Spherical triangles and Girard's Theorem Shape of Space ch 9, Polking , Great circle map 8.5.1-8.5.5, Girard's Theorem (slides)
Mon Apr 3   Spherical rotations, stereographic projection 7.5, Polking , EscherMath, stereographic projection: AMS feature column, wikipedia. Gall-Peters (West Wing), Gall-Peters, AuthaGraph, List of map projections
Wed Apr 5   Exam 2 Exam 2 from Spring 2014 and Solutions
Wed April 19   Euler's formula and regular polyhedra Regular polyhedra (cut-the-knot) and slides Euler's formula (AMS feature column), Dimensions ch 2 - 4
Thurs Apr 20   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 24   Spherical and projective geometry
Wed Apr 26   Taxicab geometry Taxi! (AMS feature column) Exploration of taxicab geometry
Mon May 1   Hyperbolic geometry 8.1 - 8.9, Shape of Space ch 10, Jos Leys, K. Mann, cut-the-knot-1
cut-the-knot-2, Escher's tiling, regular tilings
8.1.1 - 8.1.4, 8.2.1 - 8.2.3, 8.4.1, 8.6.1 - 8.6.6, Special Homework 2
Wed May 3   Classification of surfaces Shape of Space 1 - 6, 8, and Fiedorow ZIP Proof, Online resources for Shape of Space
Mon May 8   Geometry on surfaces Shape of Space ch 11-12 Geometry of the Universe
Wed May 10   Gauss-Bonnet Theorem Shape of Space ch 11-12, Givental H Gluck (slides), A Walker blog, Geometry and Imagination (see Chapters 32-35, p.59-65).
Mon May 15   Exam 3 and Review
Wed May 17   Review for final exam
May 19-26   Final Exam  

Online Resources and related links:

Attendance policy: Attendance is mandatory. Unauthorized absences from four or more classes will result in a course grade of WU (Withdrew Unofficially).

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

Important Dates: