Newton's Method and Algebraic Curves - Real Numbers and Limits Math Foundations

Explore an advanced lecture on extending Newton's method to algebraic curve intersections, focusing on the Fermat curve and Lemniscate of Bernoulli. Learn about Taylor expansions of associated polynomials, visualize tangent planes in three-dimensional space, and understand geometric interpretations. Discover how to iterate and find approximate intersections of curves. This video concludes the first part of the course, setting the stage for discussions on logical weaknesses in modern pure mathematics.

Intro to Newton's method
Fermat curve
Tangent plane to Fermat curve
Geometric Interpretaions
Lemniscate of Bernoulli
Taylor polynumbers
2D picture of Fermat curve and Lemniscate
Iterating to find approximate meets of curves