Spherical Geometry and Its Applications

1st Edition

Marshall A. Whittlesey

Chapman and Hall/CRC
August 26, 2019 Forthcoming
Textbook - 316 Pages - 123 B/W Illustrations
ISBN 9780367196905 - CAT# K418013
Series: Textbooks in Mathematics

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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. At the same time, the author wrote this book so that 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.


  • A well-rounded introduction to spherical geometry and its practical applications in a mathematically rigorous form
  • The book uses the axiomatic method, but also shows how the subject can be approached with quaternions
  • Provides several proofs of some theorems which are appealing 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
  • Poses many problems based on propositions from the ancient text Sphaerica of Menelaus
  • Brings all these ideas under one title in a way that has not been done before



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