Explore the historical development of Cartesian geometry and its impact on mathematics in this 25-minute lecture. Delve into the contributions of Descartes and Fermat in the 17th century, examining how their work merged numbers and geometry. Investigate conics, cubics, Bezout's theorem, and the early stages of projective geometry. Analyze the ancient Greek approach to geometry and discuss challenges in understanding the continuum, particularly regarding irrational numbers and decimal expansions. Learn about pi and its continued fraction approximations. Gain insights into the computational approach to Euclidean geometry and its significance in mathematical history.