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
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.
