Description

Book Synopsis

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 app

    Table of 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

Spherical Geometry and Its Applications

    Product form

    A Paperback by Marshall Whittlesey

    £999.99

    Includes FREE delivery

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      Book details

      Publisher Chapman & Hall/CRC
      Published 1/21/2023 12:01:00 AM
      ISBN-13 9781032475370
      978-1032475370
      ISBN-10 1032475374
      Also in:
      Mathematics Philosophy of mathematics

      Description

      Book Synopsis

      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 app

        Table of 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

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