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The author introduces spherical geometry and it practical applications in a mathematically rigorous form. Readers will see how the axiom system for plane geometry can be modified in certain ways to produce a completely different geometric world.
The author introduces spherical geometry and it practical applications in a mathematically rigorous form. Readers will see how the axiom system for plane geometry can be modified in certain ways to produce a completely different geometric world.
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Autorenporträt
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.
Inhaltsangabe
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
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
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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