While there are many textbooks presenting a pure or theoretical approach to geometry and many monographs investigating a single aspect of applied geometry, it is difficult to find a wide-angle view of applied geometry. The purpose of this collection is to give as broad a picture as possible of the applications of geometry. At the same time, since the papers in this collection have been written by pioneers and leading experts in each of the fields represented, the reader is assured of seeing the creativity, depth, and rigor that is an essential part of any successful application of mathematical knowledge.
This collection will be a rich resource for the geometry instructor, whether as a supplement to standard textbook material, reference material for student reports and projects, or as the starting point for a research program. The papers vary in difficulty, but are accessible to anyone having a college-level acquaintance with geometry. It is hoped that this volume will open many new worlds for all lovers of geometry.
The papers in this volume show applications of geometry to many different areas:
Art and Architecture
Engineering (robotics, structural engineering, Geographical Information Systems, and medical imaging)
Decision-Making Processes (voting and computer learning)
Mathematics (number theory, optimization, and graph theory)
Science (quantum mechanics and crystallography)
Table of Contents
Part 1: Art and Architecture
Spirals and the Rosette in Architectural Ornament, Kim Williams
Sun Disk, Moon Disk, Paul Calter
Façade Measurement by Trigonometry, Paul Calter
A Secret of Ancient Geometry, Jay Kappraff
Part 2: Vedic Civilazation
Square Roots in the Śulba, Sūtras, David W. Henderson
Applied Geometry of the Śulba, Sūtras, John F. Price
Part 3: The Classroom
Ethnomathematics for the Geometry Curriculum, Marcia Ascher
Education with Fascination: Teaching Descriptive Geometry with Applications, Marina V. Pokrovskaya
Part 4: Engineering
Making Measurements on Curved Surfaces, James Casey
Mathematics to the Aid of Surgeons, Ramin Shahidi
The Geometry of Frameworks: Rigidity, Mechanisms and CAD, Brigitte Servatius
Geometry and Geographical Information Systems, George Nagy
On the Other Hands: Geometric Ideas in Robotics, Bud Mishra
Part 5: Decision-Making Processes
Decisions through Triangles, Donald G. Saari
Geometry in Learning, Kristin P. Bennett and Erin J. Bredensteiner
Part 6: Mathematics and Science
The Geometry of Numbers, Antonie Boerkoel
Statistical Symmetry, Charles Radin
Three-Dimensional Topology and Quantum Physics, Louis H. Kauffman
Bridge between Geometry and Graph Theory, Tomaž Pisanski and Milan Randić
Polytopes in Combinatorial Optimization, Thomas Burger and Peter Gritzmann
About the Editor
Catherine Gorini is primarily interested in making mathematics, especially geometry and its applications, accessible to all students. Her research interests include geometry and its applications, connections between mathematics and the visual arts, the use of technology in mathematics education, and the relationship between consciousness and mathematics. She is on the faculty of Maharishi University of Management in Fairfield, Iowa, where she is a professor of mathematics and chair of the Department of Mathematics. Her doctoral degree from the University of Virginia is in algebraic topology.
Reviewed by Randall J. Swift
Geometry is the mathematical study of shape and form. Its ancient origins are found in such practical applications as surveying and architecture, while today, geometry is applied to such diverse areas as DNA analysis, quantum physics, and decision theory.
Geometry at Work is a collection of highly readable papers in applied geometry. The papers are organized according to area of application. The collection begins with a very interesting and well-written introduction on the nature of applications of knowledge. This philosophical discussion provides a framework and sets the tone for this broad collection of papers.
The first part of the collection contains papers on Art and Architecture, where several nice articles on the geometry of architectural ornamentation can be found. The paper by P. Calter on Trigonometry and Façade Measurement has several nice elementary applications of trigonometry, which can be used to supplement a course in trigonometry.
The collection then proceeds with some interesting historical work on the geometry of the Vedic civilization. David Henderson's work on square roots in the Sulbasutras is very enlightening for its historical context. Continued...