Spherical Geometry And Its Applications 1st Edition by Marshall A Whittlesey ISBN 0367196905 978-0367196905

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Product details:

ISBN 10: 0367196905 

ISBN 13: 978-0367196905

Author: Marshall A. Whittlesey

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.

Table of contents: 

Review of three-dimensional geometry

Geometry in a plane

Geometry in space

Plane trigonometry

Coordinates and vectors

The sphere in space

1. Great circles
2. Distance and angles
3. Area
4. Spherical coordinates

Axiomatic spherical geometry

1. Basic axioms
2. Angles
3. Triangles
4. Congruence
5. Inequalities
6. Area

Trigonometry

1. Spherical Pythagorean theorem and law of sines
2. Spherical law of cosines and analogue formula
3. Right triangles
4. The four-parts and half angle formulas
5. Dualization
6. Solution of triangles

Astronomy

1. The celestial sphere
2. Changing coordinates
3. Rise and set of objects in the sky
4. The measurement of time
5. Rise and set times in standard time

Polyhedra

1. Regular solids
2. Crystals

Spherical mappings

1. Rotations and reflections
2. Spherical projections

Quaternions

1. Review of complex numbers
2. Quaternions: Definitions and basic properties
3. Application to the sphere
4. Triangles
5. Rotations and reflections

Selected solutions to exercises

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Tags: Marshall A Whittlesey, Spherical Geometry, Applications