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The Mathematical Mechanic: Using Physical Reasoning to Solve Problems 1st Edition

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Mark Levi (Author)
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Mark Levi (Author)
3.9 out of 5 stars 16 customer reviews
ISBN-13: 978-0691140209
ISBN-10: 0691140200
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Product Details

  • Hardcover: 200 pages
  • Publisher: Princeton University Press; 1 edition (July 26, 2009)
  • Language: English
  • ISBN-10: 0691140200
  • ISBN-13: 978-0691140209
  • Product Dimensions: 9.4 x 6.3 x 0.9 inches
  • Shipping Weight: 1.1 pounds
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #724,960 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

111 of 114 people found the following review helpful
Two streams of thought are unified at last!
By Peter Haggstrom on July 31, 2009
Format: Hardcover Verified Purchase
Mark Levi's book "The Mathematical Mechanic" is a wonderful attempt to integrate physical reasoning with mathematical reasoning. These two strands have historically run in parallel and only occasionally have they been united at least at a pedagogical level. There seems to be a trend among Russian mathematicians particularly in the area of differential equations whereby they use physical reasoning to illuminate the more abstract mathematical approaches that are taken. V I Arnold is an example someone who has been known to integrate the two approaches. Perhaps Levi's Russian roots explain some of the impetus for this book. As mathematics becomes more and more specialised I fear that fewer mathematicians have the time or even inclination to think about the interconnections between physical reasoning and their own area. Levi's book is an antidote to that trend and he is to be congratulated for his efforts.

What Levy does is to take a large number of mathematical problems/theorems and show how physical reasoning using concepts such as conservation of energy, torque, resolution of forces, etc can be used to solve what are quite fundamental problems/theorems. In Chapter 2 he uses essentially torque concepts to prove the Pythagorean theorem be a thought experiment involving a right angled prism sitting in a water filled fish tank but attached to a spindle so it can rotate. The fact that it doesn't (ie there is zero net torque) leads directly to Pythagoras' Theorem.

Many of the problems turn upon one very basic physical principle and some careful reasoning about how that physical principle applies.Read more ›
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16 of 17 people found the following review helpful
What if Pythagoras had met Newton?
By Joseph Horton on November 9, 2009
Format: Hardcover Verified Purchase
I loved geometry, thought it was the greatest thing since forever. The way I proved theorems was to visualize the constructs in motion. It made the stuff come alive for me, and I saw relationships that, well, others didn't seem to appreciate.

Levi does this over and over again, but instead of merely making moving parts, he assigns the physical to what is otherwise purely mathematical. In addition to the stroll down the memory lane of my thought processes--and a reassurance that at least one other person the universe does this as well--it showed a few new ways of looking at commonplace things--like Pythagoras' theorem. He proves it using torques--torques?????--yeah, torques. Yet another proof involves concentric circles. Just read it--it's clever as anything. I grant you that I had to look at most of the analogies a couple times to get them, but get them I did.

It's a great way to spend a few hours. My bet is that this will be most useful to math and physics teachers. Is everything about physics and math intuitive? Certainly not, but enough is that having a strong sense of it is useful. It took my intuition to the next level.
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13 of 14 people found the following review helpful
Very Original and Thought-Provoking
By George Poirier on December 24, 2009
Format: Hardcover
In this unusual book, the author discusses mathematical formulas and theorems using purely physical arguments, thus eliminating the usual detailed mathematical approaches. Some of the mathematical subject areas that are discussed include geometry, conics, integration and complex variables. Some of the physical disciplines that are used are mechanics, electricity, fluid dynamics and statics and optics. I found the level of difficulty to vary throughout the book; much of the material is clear, simple and really quite fascinating, while some of it is rather complex, significantly more challenging and often quite difficult to follow, i.e., real head-scratchers. What didn't help in the latter category were the several editorial mistakes which became rather annoying in the long run. The writing style is friendly, authoritative and generally clear but undoubtedly assumes a certain level of mathematical sophistication on the part of the reader. In my view, this is a book better suited for careful study at one's own pace rather than be leisurely read as one would a popular science/math book or a novel. Consequently, serious math/science buffs could certainly enjoy perusing this book and learn a great deal from it; however, it could also be used by math/physics students as a supplementary reference in an advanced math or physics course (as suggested by the author).

As a final note, I disagree with the author's statement that this book "should appeal to ... many people who are not interested in mathematics because they find it dry or boring". Although I understand (and agree with) the author's implication that mathematics is very far from being dry and boring, I would expect that most of the people he refers to would have avoided mathematics in their lives and would thus be unwilling to read this book in the first place, or be unable to follow most of the discussions presented if they did try to read it.
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10 of 13 people found the following review helpful
A new way of looking at math
By Lance C. Hibbeler on November 12, 2009
Format: Hardcover Verified Purchase
In "The Mathematical Mechanic," Levi explains his (mostly his, but apparently a few others) way of reasoning behind various mathematical proofs. Rather than pages of algebra or calculus, a lot of mathematical things can be proved by relatively simple physical arguments, such as force and moment equilibrium, or the behavior of linear circuit components like resistors and capacitors. Such "mathematical things" include the Pythagorean theorem, inequalities, minimization problems, differential geometry, and complex variables. I have a pretty good mechanical intuition thanks to my training as an engineer, so a lot of the proofs clicked instantly with me...the physical line of reasoning espoused by Levi makes the math easier to understand. Well no, the math is still the same, but the trip to the answer is done in terms of things that are easy for me to understand and visualize, rather than just equations on the page.

This short book is a relatively quick and easy read. Levi's style is very informal, almost to the point of conversational. You do need to be a little versed in mathematics to understand what's going on, i.e. why would you care about computing integrals if you don't know what an integral is?, but Levi doesn't explicitly calculus in his proofs. If you don't have the background, or it's been a while since you've used any of it, Levi has provided a nice summary in the appendix of the book. I would recommend this for mathematicians, physicists, and engineers. It certainly expands your line of thinking.

Aside: after reading the book, I'm left somewhat puzzled. In physics, we use math to describe physical principles. Physics is not the math we use to solve its problems, though the two subjects are undoubtedly and eternally married.Read more ›
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Most Recent Customer Reviews

Five Stars

love it!

Published 4 months ago by Efren I.
Elegant solutions and deep insight in math- from an intuitive point of...

What a great book. Ranks up there with Polya in terms of real world value and insight. If you're in a technical field, read this. Everyone will learn something.

Published 5 months ago by J. Melanson
I think better pictures and a bit more detailed explanations would...

Very enlightening, but it often takes a long time to understand what he is saying. I think better pictures and a bit more detailed explanations would make it a must have book.

Published 14 months ago by mate wierdl
A Textbook for a Course in No-Logic 101

Not a Mathematics book. Not a Physics Book. Not a Science Book. A collection of bizarre claims. Based on the infantile premise that If A implies B, then B is so self-evident that... Read more

Published 15 months ago by Vic Dannon
Awesome!

Interesting and thought provoking reading material. I pick this up any time I want to wake up my brain. Thanks for an awesome read!

Published 23 months ago by emerald woulf
A wonderful way to think

I have two copies of this wonderful book - one for home and one for my office. I've always appreciated "picture proofs" and other intuitive methods
for solving problems and... Read more

Published on December 10, 2010 by Geardaddy
Great concept, wrong examples

I really wanted to like this book. Its still a good book in terms of the idea is trying to convey. However the examples given in the book are not usefull at all for anyone with at... Read more

Published on July 25, 2010 by A. Martinez
Mathematical Mechanic gives Physics a bad name.

From reading other reviews, I thought that this book would help me in my transition from sophomore to junior level in the major of physics by giving me more tools to approach a... Read more

Published on June 22, 2010 by Chris C. Haddock
MATH, PHYSICS AND MECHANICS - SUCH BEAUTY

The idea of bringing conceptual math with physics and mechanics is worth. The world is visual and mechanical therefore some apparently hidden concepts in math are explored in a... Read more

Published on April 30, 2010 by Jairo Ap Martins
The Fishy "Fish Tank" Proof of the Pythogoras Theorem

Interesting read, but what if the Fish tank is built out of a scalene triangle. According to the logic in book, you can prove a*a + b*b = c*c for any triangle. Read more

Published on January 13, 2010 by Krish Mohan

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