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Book Description
Consider a scaffolding that is constructed by bolting together rods and beams. The ultimate question is whether the structure is strong enough to support the workers and their equipment. This is the problem that motivates the area of mathematics known as rigidity theory. The purpose of this book is to develop a mathematical model for the rigidity of structures. In fact the author develops three distinct models in which the structure under consideration is modelled as a framework. These models are the degrees of freedom model and two models based on quadratic equations and linear equations respectively. The author shows that all three of these models agree except for a very small class of specially constructed frameworks. This is a theory with significant practical applications and will be of interest to a wide range of people including those studying graph theory or mathematical modelling.
About the Author
Jack Graver earned his PhD from Indiana University. After two years at Dartmouth College as a John Wesley Research Instructor, he came to Syracuse University where he has been for 35 years. He has published research papers in design theory,integer and linear programming and in several different areas in graph theory. He has co-authored three books: two graduate level texts and an elementary level book on group theory and graph theory for students of architecture. In 1993 he was awarded a Certificate of Meritorious Service by the The Mathematical Association of America. . Starting in the early 60s, he has taught a variety of summer workshops for high school teachers; in Indiana, New York, the Virgin Islands and England.
Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures (Dolciani Mathematical Expositions),Jack Graver,The Mathematical Association of America,0883853310,Engineering - Civil,General,Mathematical models,Mathematics,Mathematics / Applied,Science/Mathematics,Stability,Strength of materials,Applied,Combinatorics & graph theory,Graph theory,Mathematical foundations,Mathematics / Combinatorics,Mathematics for scientists & engineers
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