MATH 228

Classical Geometry

McGill University

This course is designed to reintroduce classical Euclidean geometry to tomorrow’s teachers. Topics include: Axioms and Euclid’s Elements, the triangle theorem, the Pythagorean Theorem and its extensions, basic constructions and similar triangles, Thales’ theorems and cyclic quadrilaterals, the centers of triangles, the nine-point circle, conic sections and analytic geometry, the prismatoid formula, the Platonic solids, non-Euclidean geometries.
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24HR Notes for MATH 228

Available 24 hours after each lecture

Thomas F Fox

MATH 228 Syllabus for Thomas F Fox — Fall 2018

Course Outline (2018)
Instructor: Tom Fox, Burnside Hall 1243,
Office Hours: Tuesday 10:30-13:00 (provisional) or by appointment
Textbook: None. Notes and readings will be posted on line. References are listed below.
Tools: The student will need a standard school geometry set with a ruler and compass.
Short course description: For twenty-two centuries geometry was considered one of the cornerstones of
civilization and an essential element of each individual’s intellectual development. Famously, above the door
of Plato’s Academy was written “Let no one ignorant of geometry enter here.” Sadly, our schools today have
set aside geometry in favour of memorized algebraic formulas and computer-science, thus depriving students of
the power of deductive reasoning and the beauty of geometric visualization. This course is designed to
reintroduce classical Euclidean geometry to today’s students, that this ancient art be not lost to future
Textbook: Notes and readings will be posted on line. References are listed below.
Method of evaluation: Three quizzes in class (60%) and a final exam (40%)
Axioms and Euclid’s Elements
The first few theorems and the triangle theorem
The Pythagorean Theorem and its extensions
Basic constructions and similar triangles
Thales’ theorems and cyclic quadrilaterals
The centers of triangles
The nine-point circle
Conic sections and analytic geometry
The prismatoid formula
The Platonic solids
Non-Euclidean geometries
1. A School Geometry. Hall & Stevens (MacMillan, 1943)
2. Euclid’s Elements. T. Heath, trans. and ed. (Dover, 1956)
3. Introduction to Geometry. H. S. M. Coxeter and S. L. Greitzer (MAA, 1967)
Additional information:
1. In accordance with McGill’s Charter of Student Rights, students in this course have the right to submit
in English or in French any written work that is to be graded.
2. In the event of extraordinary circumstances beyond the University’s control, the content and/or
evaluation scheme in this course is subject to change.
3. McGill University values academic integrity. Therefore all students must understand the meaning and
consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct
and Disciplinary Procedures (see for more information).

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