Spherical Geometry and Its Applications

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 geometryGeometry in a planeGeometry in spacePlane trigonometryCoordinates and vectorsThe sphere in spaceGreat circlesDistance and anglesAreaSpherical coordinatesAxiomatic spherical geometryBasic axiomsAnglesTrianglesCongruenceInequalitiesAreaTrigonometrySpherical Pythagorean theorem and law of sinesSpherical law of cosines and analogue formulaRight trianglesThe four-parts and half angle formulasDualizationSolution of trianglesAstronomyThe celestial sphereChanging coordinatesRise and set of objects in the skyThe measurement of timeRise and set times in standard timePolyhedraRegular solidsCrystalsSpherical mappingsRotations and reflectionsSpherical projectionsQuaternionsReview of complex numbers Quaternions: Definitions and basic propertiesApplication to the sphereTrianglesRotations and ReflectionsSelected solutions to exercises