Trigonometry, Geometry, and the Conception of Space

Book excerpt: "Trigonometry, Geometry, and the Conception of Space is primarily a textbook for students of architecture, design, or any other subject that requires a strong, practical understanding of measurement. Topics that are traditionally included for future calculus students have been replaced with a study of three-dimensional space and geometry. The first portion of the book focuses on pure trigonometry: sets and numbers, the six trigonometric functions and their inverses, and applications. The second portion covers more geometric topics like cylindrical and spherical coordinate systems, conic sections, and quadric surfaces. The material emphasizes alternative ways to describe points in space and how to transfer between them. Written for highly visual courses exploring three-dimensional space and the objects that lie within it, Trigonometry, Geometry, and the Conception of Space offers fresh, modern instruction for classes in architecture, graphic design, and mathematics. Paul Tokorcheck earned his Ph.D. in mathematics at UC Santa Cruz, with research interests in group representations, number theory, and Lie theory. He is now a lecturer with the Department of Mathematics at Iowa State University. Apart from mathematics, Dr. Tokorcheck's life journey has taken him through a variety of jobs, from cooking in award-winning kitchens of California, to teaching high school in northern Ghana, to resettling refugees from the civil wars in Liberia and Sierra Leone."