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Status:
Available5.0
21 reviewsISBN 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.
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
1 Review of three-dimensional geometry
1 Geometry in a plane
2 Geometry in space
3 Plane trigonometry
4 Coordinates and vectors
2 The sphere in space
5 Great circles
6 Distance and angles
7 Area
8 Spherical coordinates
3 Axiomatic spherical geometry
9 Basic axioms
10 Angles
11 Triangles
12 Congruence
13 Inequalities
14 Area
4 Trigonometry
15 Spherical Pythagorean theorem and law of sines.
16 Spherical law of cosines and analogue formula
17 Right triangles
18 The four-parts and half-angle formulas
19 Dualization
20 Solution of triangles
5 Astronomy
21 The celestial sphere.
22 Changing coordinates
23 Rise and set of objects in the sky
24 The measurement of time
25 Rise and set times in standard time
6 Polyhedra
26 Regular solids
27 Crystals
7 Spherical mappings
28 Rotations and reflections
29 Spherical projections
8 Quaternions
30 Review of complex numbers
31 Quaternions: Definitions and basic properties
32 Application to the sphere
33 Triangles
34 Rotations and reflections
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Tags: Marshall Whittlesey, Spherical Geometry, Its Applications
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