Explore the fascinating connections between ancient Greek mathematics and modern rational geometry in this 46-minute video lecture. Delve into Heron's formula for triangle area and its reformulation using rational quantities, known as Archimedes' theorem. Discover how the Triple Quad Formula (TQF) contains the seeds of higher-dimensional results. Learn about the historical significance of these formulas and their applications in rational geometry. Gain insights into the mathematical foundations that bridge classical and contemporary approaches to geometry.