Spherical Geometry and Its Applications

The author introduces spherical geometry and it practical applications in a mathematically rigorous form. Readers will see how the axiom system for plane geometry can be modified in certain ways to produce a completely different geometric world.

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Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject.

The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane.

Features:






A well-rounded introduction to spherical geometry



Provides several proofs of some theorems to appeal to larger audiences



Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography



Many problems are based on propositions from the ancient text Sphaerica of Menelaus