Marshall Whittlesey

Spherical Geometry and Its Applications (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 347
• Erscheinungstermin: 14. November 2019
• Englisch
• ISBN-13: 9781000627527
• Artikelnr.: 58259948

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

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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