Analytic Geometry and the Continuum - Math History - NJ Wildberger

Explore the historical development of Cartesian geometry in this 57-minute lecture from the Math History series. Delve into the 17th-century contributions of Descartes and Fermat, examining how they merged numbers and geometry to create a computational approach to Euclidean geometry. Investigate conics, cubics, Bezout's theorem, and the early stages of projective geometry. Analyze the ancient Greek influence on this mathematical advancement and consider the challenges in understanding the continuum, particularly regarding irrational numbers and decimal expansions. Examine the concept of pi and its continued fraction approximations. Gain insights into the foundations of analytic geometry and its impact on mathematical thinking.

Introduction
History
Main idea
Example
Elimination
Rene Descartes
conics
cubics
other cubics
Xus theorem
True theorem