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.

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