Spherical Geometry and Its Applications / Marshall Whittlesey

By:

Whittlesey, Marshall

Material type: Text

TextLanguage: English Publication details: Florida : CRC Press, 2020.Edition: 1st edDescription: xi, 333 p. : ill. ; 24 cmISBN:

9780367196905
9781032475370
9780429328800

Uniform titles:

Spherical Geometry and Its Applications

Subject(s):

DDC classification:

23 516.244 WHI

Contents:

Review of three-dimensional geometry Geometry in a plane Geometry in space Plane trigonometry Coordinates and vectors The sphere in space Great circles Distance and angles Area Spherical coordinates Axiomatic spherical geometry Basic axioms Angles Triangles Congruence Inequalities Area Trigonometry Spherical Pythagorean theorem and law of sines Spherical law of cosines and analogue formula Right triangles The four-parts and half angle formulas Dualization Solution of triangles Astronomy The celestial sphere Changing coordinates Rise and set of objects in the sky The measurement of time Rise and set times in standard time Polyhedra Regular solids Crystals Spherical mappings Rotations and reflections Spherical projections Quaternions Review of complex numbers Quaternions: Definitions and basic properties Application to the sphere Triangles Rotations and Reflections Selected solutions to exercises

Summary: 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

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode
Text Books	CUTN Central Library Sciences	Non-fiction	516.244 WHI (Browse shelf(Opens below))	Available		47630

Biography
Marshall A. Whittlesey is an Associate Professor of Mathematics at California State University San Marcos. He received a BS (1992) from Trinity College in Connecticut, and a PhD from Brown University (1997) under the direction of John Wermer. He was a Visiting Assistant Professor at Texas A&M University was SE Warchawski Assistant Professor at University of California San Diego (1999-2001). He has a series of research publications in functions of several complex variables.

Review of three-dimensional geometry

Geometry in a plane

Geometry in space

Plane trigonometry

Coordinates and vectors

The sphere in space

Great circles

Distance and angles

Area

Spherical coordinates

Axiomatic spherical geometry

Basic axioms

Angles

Triangles

Congruence

Inequalities

Area

Trigonometry

Spherical Pythagorean theorem and law of sines

Spherical law of cosines and analogue formula

Right triangles

The four-parts and half angle formulas

Dualization

Solution of triangles

Astronomy

The celestial sphere

Changing coordinates

Rise and set of objects in the sky

The measurement of time

Rise and set times in standard time

Polyhedra

Regular solids

Crystals

Spherical mappings

Rotations and reflections

Spherical projections

Quaternions

Review of complex numbers

Quaternions: Definitions and basic properties

Application to the sphere

Triangles

Rotations and Reflections

Selected solutions to exercises

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

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