MF79: Calculus on a cubic: the Folium of Descartes
We investigate the Folium of Descartes, viewing it both as a cubic curve in the plane, and as a surface in three dimensional space. This is an extended exercise in algebraic calculus.We parametrize it, calculate Taylor polynumbers and expansions and tangents, and interpret them both as tangent planes of tangent lines, or as tangent quadrics or tangent conics. We finish with a pleasant duality satisfied by the tangent conics.This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all
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