De Casteljau Bezier Curves in Algebraic Calculus - N J Wildberger

Explore the extension of Archimedes' Parabolic Area Formula to cubic curves in this 45-minute lecture on de Casteljau Bezier curves. Delve into the historical significance of this calculus calculation and its application to curves of the form y=a+bx+cx^2+dx^3. Discover how the formula extends to more general cubic curves with a special Archimedean property, examining the relationship between geometry and calculus. Learn about this topic within the framework of Algebraic Calculus, without the need for real numbers or infinite processes. Gain insights into the beautiful connections between control points, areas, and the point at infinity on these curves.