Explore the foundations of calculus and ancient Greek mathematics in this 54-minute lecture. Delve into the groundbreaking work of Eudoxus and Archimedes, examining their contributions to advanced calculus concepts. Discover Archimedes' formulas relating the volumes and surface areas of spheres and cylinders, his exploration of parabolic arcs, and the improved version of Heron's formula using Rational Trigonometry. Learn about Archimedes' contributions to hydrostatics and the Principle of the Lever, showcasing his true genius in mathematical and mechanical fields.