Calculus on a Cubic - The Folium of Descartes - Arithmetic and Geometry Math Foundations

Explore the Folium of Descartes in this 32-minute lecture from the MathFoundations series. Delve into an extended exercise in algebraic calculus, examining the curve both as a cubic in the plane and a surface in three-dimensional space. Learn to parametrize the curve, calculate Taylor polynumbers and expansions, and determine tangents. Interpret these concepts as tangent planes, lines, quadrics, and conics. Discover a fascinating duality satisfied by the tangent conics. Gain insights into the logical foundations of modern pure mathematics through this in-depth exploration of a classic geometric object.

Introduction
Taylor polynumbers and expansions
Tangents
Interpretation A and B
Tangent objects to a quadric
Special case: r,s lies on the cubic
Theorem Folium tangent conic symmetry