Abstract
It is impossible to map figures on the sphere onto congruent ones on the plane. Because the Earth is spherical, any flat representation of it causes distortions such that both areas and shapes cannot be conserved simultaneously, i.e., the distance cannot be preserved. The mapmaker must choose a projection method suitable for the region to be mapped and the purpose of the map. Stereographic projection is one method of making maps that preserves angles.
“Everything has beauty, but not everyone sees it.”
Confucius (551–479 BC)
“Inspiration is needed in geometry, just as much as in poetry.”
Alexander Pushkin (1799–1837)
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Lee, NH. (2020). Stereographic Projection and Inversions. In: Geometry: from Isometries to Special Relativity. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-42101-4_3
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DOI: https://doi.org/10.1007/978-3-030-42101-4_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-42100-7
Online ISBN: 978-3-030-42101-4
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