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 | The Mathematical Mechanic: |
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. Mark Levi is professor of mathematics at Pennsylvania State University. "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 Endorsements: "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 "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 "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 Subject Areas:
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