Скачать или смотреть Spherical and elliptic geometries (cont.) | Universal Hyperbolic Geometry 34 | NJ Wildberger

We continue our introduction to spherical and elliptic geometries, starting with a discussion of longitude and latitude on a sphere. We mention the close historical connections between spherical geometry and astronomy, going back to the ancient Greeks, to the Indians and to the Arabs. We explain the relationship of spherical geometry and Euclid's 5 postulates. Elliptic geometry is the result of identifying antipodal points on the sphere. Measurement on the surface of a sphere uses angles to define spherical distances, but additional functions are required. We describe Ptolemy's tables of chords and later Indian and Arab work on tables of sines. The final result is Menelaus' theorem, which first appears in the spherical setting, using chords.

Video Content:
00:10 Latitude and Longitude
10:13 Spherical geometry and astronomy
13:40 Euclid studied the sphere
25:11 Elliptic geometry
29:15 Measurement in spherical/elliptic geometries
33:22 Tables of chords
38:41 Menelaus' theorem

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