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Explore a novel approach to verifying Archimedes' parabolic area formula using Algebraic Calculus in this 39-minute lecture. Dive into the world of de Casteljau Bezier (dCB) curves and discover how this method differs from classical calculus. Learn about the Fundamental theorem in Algebraic Calculus and its application to quadratic dCB curves. Gain insights into the connections between geometry and linear algebra while exploring this more algebraic approach to calculus, where curves take precedence over functions and limits are not required. Although not a comprehensive introduction to Algebraic Calculus, this lecture provides enough foundation to understand the argument with some additional effort, preparing you for further exploration into cubics and beyond.
