The Mathematical Mechanic: Using Physical Reasoning to Solve Problems

The Mathematical Mechanic: Using Physical Reasoning to Solve Problems

by Mark Levi
     
 

Everybody knows that mathematics is indispensable to physics—imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of

Overview

Everybody knows that mathematics is indispensable to physics—imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist.

Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles.

The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.

Editorial Reviews

The Math Less Traveled
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
Mathematics Teacher
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.
UMAP Journal
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
Seed Magazine
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.
London Mathematical Society Newsletter - Nigel Steele
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.
MAA Reviews - John D. Cook
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.
The Math Less Traveled - Boris Yorgey
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.
Choice - E. Kincanon
The Mathematical Mechanic is a pleasant surprise.
UMAP Journal - Steven G. Krantz
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.
From the Publisher
One 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

London Mathematical Society Newsletter
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
MAA Reviews
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
SEED Magazine
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.
Choice
The Mathematical Mechanic is a pleasant surprise.
— E. Kincanon

Product Details

ISBN-13:
9780691154565
Publisher:
Princeton University Press
Publication date:
07/22/2012
Edition description:
Reprint
Pages:
200
Sales rank:
695,514
Product dimensions:
6.00(w) x 9.20(h) x 0.60(d)

What People are saying about this

Louis Nirenberg
This is an absolutely delightful book, full of surprises—even for mathematicians like myself—and beautifully written. It can be enjoyed by anyone, from someone just learning calculus to professional mathematicians and physicists.
Louis Nirenberg, recipient of the National Medal of Science
Philip Holmes
I know of no other book quite like this, or even similar to it. After a couple of sentences of the introduction, I was hooked. The general theme—to show how physical reasoning can illuminate mathematical ideas and simplify proofs—is very attractive. This book will appeal to math enthusiasts at all levels, from high-school students on up.
Philip Holmes, coauthor of "Celestial Encounters"
Steven Strogatz
What a fun book! Mark Levi's physical arguments are so clever and surprising that they made me laugh with pleasure, again and again. The Mathematical Mechanic is downright magical—a real treat for anyone who loves intuition.
Steven Strogatz, author of "Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life"
Gregory Somers
The Mathematical Mechanic jazzes up the old married couple, math and physics. The book breathes fresh air into the (sometimes stale) relationship and invites us to rethink familiar topics in unfamiliar ways. It disorients us in the most delightful manner. Mark Levi's razor-edge writing and gentle humor permeate every page. I will turn to this book again and again for inspiration on teaching math to high school students.
Gregory Somers, State College Area High School, recipient of the Edyth May Sliffe Award for Distinguished Mathematics Teaching
Nahin
This book is a fresh, insightful, and highly original presentation of mathematical physics that will appeal to a broad spectrum of readers. I have not seen anything like it before. It is a book that a physicist or engineer would be proud to have written, and the fact that it has been written by a mathematician only adds to the book's authority. A definite winner.
Paul J. Nahin, author of "Digital Dice"
Nancy Kopell
This is an extraordinary book that only Mark Levi could have written. No one interested in mathematics or physics can fail to be amazed and delighted. It is witty and charming as well as deep, and accessible with very little background required—a tour de force!
Nancy Kopell, Boston University, MacArthur Fellow
Joseph Keller
This book shows how many mathematical theorems can be proved by looking at them in mechanical or geometrical terms. I found it to be very interesting and fun to read. I recommend it most enthusiastically.
Joseph Keller, recipient of the National Medal of Science
Tadashi Tokieda
The most imaginative and charming book on mechanics and geometry in the last fifty years—for lighting up tea times, for thrilling classrooms, as a present for a special friend, as company on a desert island.
Tadashi Tokieda, University of Cambridge

Meet the Author

Mark Levi is professor of mathematics at Pennsylvania State University and the author of Why Cats Land on Their Feet (Princeton).

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