Euclidean Geometry

This course exists to provide students with a classical ad fontes alternative to modern geometry courses & textbooks. During this course, students will study 5 books of Euclid’s Elements (I-III, V-VI). The vast majority of time is spent with Euclid, although two other texts are introduced to provide background, context, and perspective. The class and coursework are organized and arranged to first disorient students away from their preconceptions regarding mathematics. Next, students are immersed in a beautiful world of numbers to allow them a sense of the aesthetics of math. After those preparatory experiences, students are introduced to Euclid and learn to follow and create proofs, perform complex constructions, and think critically about the nature of geometry. In short, students will learn to think like mathematicians rather than mere computers.

Class time will be spent discussing and working out propositions. Students will be expected to work through propositions during the week and will take turns presenting the proofs to the class. Students should expect to spend an average of 1 – 1.5 hours per school day studying & working problems. During the week, students will be responsible for keeping up with weekly assignments & practice problems. Apart from the exams, students are expected to correct their own homework & assignments. To evaluate and encourage broad-scale analysis, three essays will also be assigned.

Course Objectives

To gain a more profound understanding & mastery of geometry than is possible via traditional textbooks. To learn to see mathematics as a discipline of beauty, to master the art of writing geometric proofs, to learn to think in precise and creative terms in mathematics and beyond.

Texts

• Classical Mathematics ONE (Polymath Classical Tutorials)
• Euclid's Elements (Green Lion Press edition)
• Nicomachus' Introduction to Arithmetic, Book I
• Mathematics for the Nonmathematician - Morris Kline