Shapes and Geometry of Surfaces by Mahan Mj

Explore the fascinating world of shapes and geometry of surfaces in this comprehensive lecture by Mahan Mj from the International Centre for Theoretical Sciences. Delve into a 19th-century method for understanding the various shapes encountered in space, with a focus on surfaces. Examine examples of surfaces, learn how to organize information about them, and discover their classification. Investigate key concepts in topology, including closed surfaces, Mobius strips, and the distinction between inside and outside. Gain insights into nonorientable surfaces, doughnuts, and Klein Bottles. Analyze the relationship between topology and curvature, and explore the geometry of flat planes. This 1-hour 47-minute talk, originally presented at the J.N. Planetarium in Bangalore, offers a comprehensive introduction to the shapes and geometric structures that surround us in our everyday lives.

Intro
What are surfaces
Examples of surfaces
Organizing information
Classification
Topology
Closed
Mobius strip
Outside and inside
Nonorientable surfaces
Doughnut
Klein Bottle
Topology and curvature
Geometry
Flat plane