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This introductory lecture defines core concepts in spherical geometry and relates them to points, lines, and planes in three-dimensional space. Physical models illustrate great circles, antipodal points, spherical triangles, and circles on the sphere.
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