Description
Book SynopsisDid you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? This title demonstrates how to use physical intuition to solve these and other math problems.
Trade ReviewOne of Amazon.com science editors' Top 10 list for Science, Best for 2009 One of Choice's Outstanding Academic Titles for 2009 "The Mathematical Mechanic documents novel ways of viewing physics as a method of understanding mathematics. Levi uses physical arguments as tools to conjecture about mathematical concepts before providing rigorous proofs... The Mathematical Mechanic is an excellent display of creative, interdisciplinary problem-solving strategies. The author has explained complex concepts with simplicity, yet the mathematics is accurate."--Mathematics Teacher "A most interesting book... Many of the ideas in it could be used as motivational or illustrative examples to support the teaching of non-specialists, especially physicists and engineers. In conclusion--a thoroughly enjoyable and thought-provoking read."--Nigel Steele, London Mathematical Society Newsletter "The Mathematical Mechanic reverses the usual interaction of mathematics and physics... Careful study of Levi's book may train readers to think of physical companions to mathematical problems... Mathematicians will find The Mathematical Mechanic provides exercise in new ways of thinking. Instructors will find it contains material to supplement mathematics courses, helping physically-minded students approach mathematics and helping mathematically-minded students appreciate physics."--John D. Cook, MAA Reviews "Mark Levi reverses the old stereotype that math is merely a tool to aid physicists by showing that many questions in mathematics can be easily solved by interpreting them as physical problems... Some sections of the book require readers to brush up on their calculus but Levi's clear explanations, witty footnotes, and fascinating insights make the extra effort painless."--SEED Magazine "The book is chock-full of these seemingly magical physical thought experiments involving bicycle wheels, pistons, springs, soap films, pendulums, and electric circuits, with applications to geometry, maximization and minimization problems, inequalities, optics, integrals, and complex functions... I highly recommend it to anyone who is (even slightly) interested in physics, and appreciates mathematical elegance and cleverness. It would make a great gift for almost anyone, whether a high school student or university professor, armchair physicist or professional mathematician."--Boris Yorgey, The Math Less Traveled "The Mathematical Mechanic is a pleasant surprise."--E. Kincanon, Choice "This is a delightful and unusual book that is a welcome addition to the literature. Certainly, any calculus teacher and many others of us as well will want to have it on the shelf for ready reference. It not only will enhance our teaching experience but will also teach us (the instructors) something in the process."--Steven G. Krantz, UMAP Journal
Table of Contents*FrontMatter, pg. i*Contents, pg. v*1 Introduction, pg. 1*2 The Pythagorean Theorem, pg. 9*3 Minima and Maxima, pg. 27*4 Inequalities by Electric Shorting, pg. 76*5 Center of Mass: Proofs and Solutions, pg. 84*6 Geometry and Motion, pg. 99*7 Computing Integrals Using Mechanics, pg. 109*8. The Euler-Lagrange Equation via Stretched Springs, pg. 115*9 Lenses, Telescopes, and Hamiltonian Mechanics, pg. 120*10 A Bicycle Wheel and the Gauss-Bonnet Theorem, pg. 133*11 Complex Variables Made Simple(r), pg. 148*Appendix. Physical Background, pg. 161*Bibliography, pg. 183*Index, pg. 185
