PLANE AND COORDINATE Geometry

The class will meet twice a week for one hour each time. The meetings will tentatively take place every Monday and Thursday between September 5, 2022 and May 29, 2023 (but the exact days and times are to be decided later). All sessions are recorded and available for playback and download immediately after class. Should there be enough student interest, the class may continue in the following school year. 

All sessions are $75 each; we will be meeting biweekly most of the time, with the exceptions of holidays, special event days, etc. You will be billed monthly, depending on the number of classes on each particular month. Payment can be done by Zelle, Paypal, or check. A $200 deposit must be paid by August 31, 2022. The deposit will be applied to the September tuition for all students who end up participating in the class. The deposit is non-refundable for all students that withdraw before the start of the class or within the first two weeks from the start of the class.

To guarantee that the class is running, please complete the sign-up below and pay the deposit by August 31, 2022.

We will cover fundamental results in Euclidean geometry: basic axioms and postulates, parallel lines, congruent and similar triangles and polygons (Thales' Theorem and the Fundamental Theorem of Similarity), quadrilaterals (including parallelograms, rhombi, rectangles, squares, trapezoids, and kites), right triangles (The Leg and Altitude Theorems) and the Pythagorean Theorem, circles (arcs, chords, tangents, central, inscribed, interior and exterior angles), cyclic and circumscribed quadrilaterals, the power of a point theorems, areas of plane figures, geometric inequalities, regular polygons, special parts of a triangle (medians, angle bisectors, altitudes) and the four concurrency points (incenter, circumcenter, orthocenter, and center of mass), special topics (Menelaus' Theorem, Ceva's Theorem, Van Aubel's Theorem, Stewart's Theorem, the Heron-Archimedes Formula, Brahmagupta's Formula, Ptolemy's Theorem, etc), constructions and loci, coordinate geometry, and combinatorial geometry.

• Introduction to Geometry, by Richard Rusczyk (2007 edition)  https://www.amazon.com/Introduction-Geometry-2nd-Problem-Solving/dp/1934124087/ref=sr_1_3?ie=UTF8&qid=1534228914&sr=8-3&keywords=introduction+to+geometry+by+richard+rusczyk  https://artofproblemsolving.com/store/item/intro-geometry  

You can purchase online versions of this book at the Art of Problem Solving bookstore.  

• Geometry, by Ray C. Jurgensen, Richard G. Brown, and John W. Jurgensen (2009 edition)  https://www.amazon.com/Geometry-Ray-C-Jurgensen/dp/0395977274/ref=sr_1_1?s=books&ie=UTF8&qid=1534229047&sr=1-1&keywords=jurgensen+geometry  

• Geometry for Challenge and Enjoyment, by Richard Rhoad, George Milauskas, and Robert Whipple (1991 edition)  https://www.amazon.com/Geometry-Enjoyment-Challenge-Richard-Rhoad/dp/0866099654/ref=sr_1_1?s=books&ie=UTF8&qid=1534229209&sr=1-1&keywords=geometry+for+enjoyment+and+challenge+1991  

The following books are highly recommended, but not mandatory: 

•  Lessons in Geometry, Vol 1: Plane Geometry, by Jacques Hadamard  https://www.amazon.com/Lessons-Geometry-Vol-Monograph-English/dp/0821843672/ref=sr_1_1?s=books&ie=UTF8&qid=1534229406&sr=1-1&keywords=hadamard  

• Challenging Problems in Geometry, by Alfred Posamentier and Charles T. Salkind  https://www.amazon.com/Challenging-Problems-Geometry-Dover-Mathematics/dp/0486691543/ref=sr_1_1?s=books&ie=UTF8&qid=1534229542&sr=1-1&keywords=challenging+problems+in+geometry  

• Problems in Plane and Solid Geometry, Vol 1, by Viktor Prasolov (translated from Russian)

We will start our study of Geometry in the tradition of Euclid, building our knowledge tools from basic axioms and definitions, and proceeding to prove more complicated statements (theorems, propositions, corollaries, etc). All theoretical results will be proved in class, and each will be followed by numerous examples, ranked from very easy to quite sophisticated. The handouts I prepare have all the facts proved in class, as well as exercises that will be solved during the sessions. The exercises will be selected from the above mentioned textbooks, as well as national and international mathematics competitions. Each session is followed by a homework set, ranging in length, depending on the material covered in class on a particular day. Students should expect to spend a few hours every week doing homework and reviewing the class handouts. The homework assignments and all class correspondence will be addressed to both students and their parents. All homework problems that students had difficulties with will be discussed in class.

All interested students should have completed a course in Algebra I, or have sufficient knowledge of linear equations and inequalities, ratios and proportions, and square roots. Knowledge of basic counting strategies and probability is desired, and so is knowledge of quadratic equations (factoring, the quadratic formula). The students should also be familiar with equations of lines and graphing in cartesian coordinate planes.

This is a high-end, intensive, and challenging class, so students signing up are expected to be in grades 7 and up. A student in grade lower than 7 who wishes to sign-up must provide a letter of recommendation from a school teacher or mentor that can comment on the student's academic abilities and mathematical interest.

• any student that has not been taking Geometry before, and is looking for a rigorous and challenging introduction to the subject 
• any student aiming at scoring high in national/international math competitions: AMC 8/Mathcounts/AMC 10/12/AIME/USAMO
• any student who has been taking Geometry before, but can't remember anything useful or interesting 
• any student that loves mathematics and is interested in being challenged in a real and serious geometry course