Spherical Geometry and Its Applications

Spherical Geometry and Its Applications provides a rigorous introduction to spherical geometry, with an axiomatic system and proofs using quaternions. It demonstrates how a traditional axiomatic system can be modified to create a different geometric world, illustrating its applications in the study of the surface of the Earth, stars, planets, polyhedra, mappings, and crystallography.

Format: Paperback / softback
Length: 348 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Spherical geometry, a branch of mathematics, delves into the study of shapes on a spherical surface. This comprehensive text offers a rigorous mathematical exploration of spherical geometry, making it an ideal resource for mathematics majors seeking to delve into this field. Whether readers come from diverse academic backgrounds or have a limited knowledge of mathematics, this book provides a clear and accessible introduction to spherical geometry.

The book begins by introducing an axiomatic system for spherical geometry, which serves as a foundation for the subsequent theorems and proofs. This axiomatic system allows for a systematic and logical approach to studying spherical shapes and their properties. Additionally, the book offers an alternative approach using quaternions, providing readers with a different perspective on spherical geometry.

One of the key features of this text is its comprehensive coverage of spherical geometry's applications. The author demonstrates how traditional axiomatic systems for plane geometry can be modified to create a different geometric world, yet one that is no less real than the plane's geometric world. This modification showcases the versatility and richness of spherical geometry and its potential applications in various fields.

The book includes numerous proofs of various theorems, catering to a broader audience. These proofs provide a deeper understanding of the subject and help readers grasp the intricacies of spherical geometry. Moreover, the book presents principal applications of spherical geometry, including 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.

Numerous problems are based on propositions from the ancient text "Sphaerica" of Menelaus, adding an historical and cultural dimension to the study of spherical geometry. These problems not only test readers' understanding of the subject but also encourage them to apply their knowledge in practical scenarios.

In conclusion, Spherical Geometry and Its Applications is a valuable resource for anyone interested in exploring the world of spherical shapes and their applications. With its rigorous mathematical approach, comprehensive coverage, and practical applications, this text serves as an excellent introduction to spherical geometry for mathematics majors and readers from various academic backgrounds.

Weight: 526g
Dimension: 154 x 234 x 23 (mm)
ISBN-13: 9781032475370