Infinity and Perspective - Lecture 3

Explore the mathematical concept of infinity through this third lecture in Erik Christopher Zeeman's groundbreaking 1978 Christmas Lectures series at The Royal Institution. Discover how infinity connects seemingly unrelated topics including Zeno's famous paradox of Achilles and the tortoise, Renaissance perspective painting techniques, and barbershop mathematics. Learn about three distinct mathematical contexts where infinity plays a crucial role: Greek paradoxes that challenge our understanding of motion and time, the vanishing point theory that revolutionized artistic representation of three-dimensional space on two-dimensional surfaces, and the theory of infinite sets that forms a cornerstone of modern mathematics. Examine how Renaissance artists used mathematical principles of infinity to create realistic perspective in their paintings, transforming the art world's approach to spatial representation. Understand the precise mathematical usage of infinity across different contexts, moving beyond its vague common language applications to explore its rigorous mathematical foundations. Experience the practical demonstrations and visual explanations that made this historic lecture series the first mathematics-focused Christmas Lectures in the Royal Institution's then 149-year history, inspiring a new generation of mathematicians and leading to the establishment of the Mathematics Masterclasses programme.