For millennia, geometry enjoyed a prominent role in the curriculum of the educated. It wasn’t until the launching of Sputnik in 1957 and the specter of doom from the cold war that education in math and science was reimagined for a more modern world. Ever since, the mathematical education of American children has been a straight pipeline to calculus.
While not as popular today as during the time of Euclid, Möbius, and Poincaré, the study of geometry is still valuable for building mathematical maturity, for presenting a compelling alternative to calculus, and of course, for its intrinsic beauty.
While these notes are self-contained, if you’d like to follow along, I am referring to the textbook Geometry by Brannan, Esplen, and Gray when creating these notes.
Prerequisites: High-school level algebra. Some linear algebra might help although I will introduce concepts as needed.
Conics Review - In this chapter, we study conic sections for their own interest. We will see them frequently throughout later chapters.
Conic Sections and Conics - In this section, we investigate how to describe conic sections.