Explore the fundamentals of spherical and elliptic geometries in this 32-minute video lecture from the Universal Hyperbolic Geometry series. Delve into key concepts such as great circles as lines, antipodal points, spherical triangles, and circles on a sphere. Examine the relationship between points, lines, and planes in three-dimensional space, with physical models illustrating these ideas. Compare spherical geometry to Euclidean geometry, noting how lines represent the shortest path between two points. Investigate the properties of circles on a sphere and discover how spherical geometry approximates Euclidean geometry on larger spheres. Gain valuable insights into these non-Euclidean geometries, laying the groundwork for further study in universal hyperbolic geometry.
Overview
Syllabus
Introduction
The sphere
Basic definitions
Spherical geometry
In Euclidean geometry, a line is shortest path between two points
The sphere in three-dimensional space
Circles on the sphere
On a big sphere, the geometry looks close to Euclidean
Taught by
Insights into Mathematics
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