A Brief History of Geometry III - The 19th Century - Sociology and Pure Mathematics

Explore the pivotal developments in geometry during the 19th century in this 53-minute lecture from the Insights into Mathematics series. Gain an overview of major advancements including Inversive Geometry, Projective Geometry, Non-Euclidean Geometry, and Complex Geometry. Discover why this period is considered a golden age for geometry and learn about its subsequent decline in the 20th century. Follow the progression from the introduction of circle geometry to the exploration of infinity, projective concepts, and non-Euclidean models. Examine the contributions of E. Beltrami and delve into the realm of complex geometry. Suitable for a non-mathematical audience, this simplified overview provides valuable insights into the historical evolution of geometric thought.

Introduction
A geometry of circles!
Infinity and projective geometry
Non-Euclidean geometry
E. Beltrami
Complex geometry
Complex geometries