Spherical Geometry and Its Applications

AvMarshall Whittlesey

Inbunden, Engelska, 2019

Del i serien Textbooks in Mathematics

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682 kr

Beskrivning

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

Produktinformation

Utgivningsdatum:2019-08-15
Mått:156 x 234 x 20 mm
Vikt:640 g
Format:Inbunden
Språk:Engelska
Serie:Textbooks in Mathematics
Antal sidor:335
Förlag:Taylor & Francis Ltd
ISBN:9780367196905

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Mer om författaren

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.

Innehållsförteckning

Review of three-dimensional geometryGeometry in a planeGeometry in spacePlane trigonometryCoordinates and vectorsThe sphere in spaceGreat circlesDistance and anglesAreaSpherical coordinatesAxiomatic spherical geometryBasic axiomsAnglesTrianglesCongruenceInequalitiesAreaTrigonometrySpherical Pythagorean theorem and law of sinesSpherical law of cosines and analogue formulaRight trianglesThe four-parts and half angle formulasDualizationSolution of trianglesAstronomyThe celestial sphereChanging coordinatesRise and set of objects in the skyThe measurement of timeRise and set times in standard timePolyhedraRegular solidsCrystalsSpherical mappingsRotations and reflectionsSpherical projectionsQuaternionsReview of complex numbers Quaternions: Definitions and basic propertiesApplication to the sphereTrianglesRotations and ReflectionsSelected solutions to exercises