Parametrized Curves and Algebraic Curves - Differential Geometry

Explore the fascinating world of parametrized and algebraic curves in this 41-minute lecture on differential geometry. Delve into the ancient Greek origins of conic parameterization before examining more complex algebraic curves like Fermat's cubic, the Folium of Descartes, and the Lemniscate of Bernoulli. Discover the 17th century's obsession with motion through Newton's laws and investigate intriguing curve-generating mechanisms, including the four-bar linkage and Watt's linkage. Gain valuable insights into the mathematical principles underlying these concepts and their historical significance in the development of geometry and mechanics.

Introduction
Unit circle
Rational parameterization
Algebraic curves
Descartes cubic
Fourbar linkage
Watt linkage