Abstract
Spherical geometry is almost as old as Euclidean geometry. In fact, the word geometry means “measurement of the Earth,” and the Earth is (more or less) a sphere. The ancient Greek geometers knew that the Earth was spherical. Navigation motivated the study of spherical geometry because, even 2000 years ago, the fact that the earth is curved had a noticeable effect on cartography. In spherical geometry, the “points” are points on the surface of the sphere. We are not concerned with the “inside” of the sphere.
“The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.”
Isaac Newton (1642–1727)
“Geometry is the art of correct reasoning from incorrectly drawn figures.”
Henri Poincaré (1854–1912)
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Lee, NH. (2020). Sphere. In: Geometry: from Isometries to Special Relativity. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-42101-4_2
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DOI: https://doi.org/10.1007/978-3-030-42101-4_2
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