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

Geometry MTH 329 Spring 2021

Monday & Wednesday, 12:20 pm - 2:15 pm

Prof. Ilya Kofman


Textbook: Geometry: The Line and the Circle by Maureen T. Carroll and Elyn Rykken. Print ISBN: 978-1-4704-4843-1 and Electronic ISBN: 978-1-4704-5063-2. You must also buy an (inexpensive) compass and ruler.

You are expected to be familiar with high-school geometry; for review, see, a free online math textbook for high-school geometry.

Homework: Assignments will be announced in class, usually referring to this website. I highly recommend working jointly on homework problems with fellow students.

Labs: We will use GeoGebra, a free interactive geometry app. The authors have provided a supplemental PDF of lab projects called GeoGebra Labs. Follow their instructions to install GeoGebra Classic 6 at Then download a zip file of GeoGebra Lab starter files, and extract them on your computer.

Exams: There will be two in-class exams: Exam 1 on Monday, March 8 and Exam 2 on Monday, April 19. Without exception, you must take the final exam at the time scheduled by the college.

Grading: The course grade will be determined (subject to changes announced in class) by your online participation and by your scores on homework, labs, exams and final exam.

Help: My office hours are on Mondays and Wednesdays 3:30pm - 4:45pm. Email is the fastest way to contact me.

How to Study: (1.) Attend class (attendance is mandatory).  (2.) Read the relevant sections and websites after class.  (3.) Do the homework and labs. Leave time to think--do not put homework off until it is due!  (4.) Use the Blackboard discussion board or visit me during office hours with any questions.  (5.) To study for a math exam, you must DO MORE PROBLEMS from notes, review materials and the textbook.

Schedule of lectures and homework (subject to changes announced in class). Section and problem numbers refer to Geometry:The Line and the Circle.

Date Topic Reading Homework
Mon Feb 1   Introduction to Euclid's Elements, and constructions Ch. 1 and Ch. 2 1.3.1, Lab 1
Wed Feb 3   Book 1: Neutral Geometry Ch. 3.1 3.1.1, 3.1.7, 3.1.8, 3.1.10, Lab 2
Mon Feb 8   Book 1: Neutral Geometry Ch. 3.2, 3.3, Triangle Inequality Thm 3.2.6, 3.2.8, 3.2.10
Wed Feb 10   Book 1: Neutral Geometry Ch. 3.3, Quads Venn diagram, Quad properties, Compass constructions 3.3.7-9, 3.3.12-14, Lab 3
Wed Feb 17   Vectors and dot product Stillwell ch4, Math Corner Vector HW
Mon Feb 22   Spherical geometry Ch. 4.1-4.4, Ryan, Polking, Dimensions Ch 1, Spherical Geometry, MH370 search circle 4.4.1, 4.4.6, Sphere HW
Wed Feb 24   Spherical triangles and Girard's Theorem Ch. 4.5, Exterior Angles Thm, Girard's Theorem (slides)
Mon Mar 1   Stereographic projection and maps Ch. 4, Gall-Peters (West Wing), Stereographic projection (AMS feature column), Dimensions Ch 9, Peters vs Mercator, Gall-Peters (wikipedia), AuthaGraph, Winkel-Tripel, List of maps
Wed Mar 3   Taxicab geometry Ch. 5, Taxi! (AMS feature column)
Mon Mar 8   Exam 1
Wed Mar 10 Axiomatic geometry Ch. 6
Mon Mar 15   Euclidean geometry: parallel lines, area Ch. 7.1-7.5 7.1: 2-4,   7.4: 5-6
Wed Mar 17   Pythagorean Theorem, geometric algebra Ch. 7.6, Ch.8, Euclid's proof, gogeometry, Pythagorean triples, squaring a rectangle 7.6: 6, 10,   8.1: 9, 10,   Lab 4
Mon Mar 22   Thales' Theorem and Similarity Ch. 9, cut-the-knot, Givental 9.2: 4, 8, 10   9.3: 2, 4
Wed Mar 24   Pythagorean Theorem: other proofs cut-the-knot,
Mon Apr 5   Circles Ch. 10, Eratosthenes 10.2.11, 10.3.2, 10.3.14, 10.4.8, Lab 5
Wed Apr 7   Concurrence in triangles Ch. 11.1-11.2, GeoGebra Concurrence, Ceva's Theorem Lab 6
Mon Apr 12   Regular polygons and constructibility Ch. 11.4-11.5, Ch. 16, Regular pentagon Lab 7, Lab 11
Wed Apr 14   Review
Mon Apr 19   Exam 2
Wed April 21   Isometries, 3-Reflections Theorem Ch. 15.1-15.3, Applet Lab 9
Mon Apr 26   Classification of Euclidean Isometries Ch. 15.1-15.3, cut-the-knot, Wikipedia Lab 10
Wed Apr 28   Spherical 3-Reflections Theorem, Hyperbolic plane Ch. 12, Poincare disk, Escher, Escher gallery, Taimina, soccer, kale Lab 8
Mon May 3   Hyperbolic tessellations Joyce, Tilings-1, Tilings-2, Jos Leys, Series-Wright, Hatch
Wed May 5   Inversions, Isometries of hyperbolic plane Ch. 15.4-15.5, cut-the-knot-1, cut-the-knot-2, Cheritat
Mon May 10   Hyperbolic geometry Ch. 13
Wed May 12   Euler's formula and regular polyhedra Regular polyhedra (cut-the-knot) and slides, Euler's formula (AMS feature column), Givental, Dimensions ch 2 - 4
Mon May 17   Review for final exam
May 19-24   Final Exam  

Online Resources and related links:

Attendance policy: Attendance is mandatory. Unauthorized absences from three 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: