## Prof. Ilya Kofman

Office:   1S-209   phone: (718) 982-3615
Email:   ikofmanmath.csi.cuny.edu
Website:   http://www.math.csi.cuny.edu/~ikofman/
 Course Time and Place: Mondays:    4:40pm - 6:20pm   in 1S-107 Wednesdays:   4:40pm - 6:20pm   in 1S-219

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: 30% Exam 1 + 30% Exam 2 + 40% Final Exam.

Help:  My office hours are on Mondays 1:30-3:00pm and Wednesdays 3:30-4:30pm, in my office, 1S-209.

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.

 Date Topic Reading HW 1 Feb 1 Euclidean constructions 1.1 - 1.3 1.2.1-1.2.3, 1.3.3-1.3.6 2 Feb 3 Thales' Theorem, similar triangles 1.4 - 1.5 1.4.1-1.4.4 3 Feb 8 Parallel and congruence axioms 2.1 - 2.2, Properties of quadrilaterals. 2.1.1-2.1.5, 2.2.1-2.2.3 4 Feb 10 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 5 Feb 17 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 6 Feb 18 Pythagorean Theorem revisited, other proofs 2.8, cut-the-knot, gogeometry, Givental 2.8.1-2.8.3 7 Feb 22 Coordinates 3.1 - 3.5 3.2.1-3.2.6, 3.3.1, 3.4.1-3.4.3 8 Feb 24 Concurrence in triangles Chords, arcs and angles in a circle regentsprep and mathopenref Regents Exam 9 Mar 1 Geometry on NY Regents Exam regentsprep and mathopenref 10 Mar 3 Review F07 Exam 1, S09 Exam 1 11 Mar 8 Exam 1 S10 Exam 1 12 Mar 10 Isometries, Three Reflections Theorem 3.6 - 3.8 3.6.1-3.6.4, 3.7.1-3.7.3 13 Mar 15 Classification of plane isometries, group of isometries cut-the-knot, wikipedia, 7.1 7.1.1-7.1.3 14 Mar 17 Vectors 4.1 - 4.2 4.1.3-4.1.4, 4.2.1-4.2.2 15 Mar 22 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 16 Mar 24 Matrices, transformations, isometries 4.7, 7.2 7.2.1-7.2.6 17 Apr 7 Spherical geometry 7.4 - 7.5, Polking, Strogatz (NYT article) 7.4.1-7.4.5 18 Apr 12 Spherical triangles and Girard's Theorem Shape of Space 9, Polking Dimensions Lectures 1 and 9 19 Apr 14 Review Review Problems for Exam 2 20 Apr 19 Exam 2 S10 Exam 2 S09 Exam 2, S09 Exam 2 solutions 21 Apr 21 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 22 Apr 26 Hyperbolic geometry introduction 8.1 - 8.9, Shape of Space 10, 15, Isometries of hyperbolic plane Escher's hyperbolic plane, cut-the-knot1, cut-the-knot2 23 Apr 28 Euler's formula and regular polyhedra Regular polyhedra classified using the Euler Characteristic Euler's formula (AMS feature column) 24 May 3 Classification of surfaces Shape of Space 1 - 6, 8, and Fiedorow Online resources for Shape of Space 25 May 5 Geometry on surfaces Shape of Space 7, 11 26 May 10 Gauss-Bonnet Theorem and Euler Characteristic Shape of Space 12 27 May 12 Review 28 May 17 Review