The Mathematical Mechanic Using Physical Reasoning To Solve Problems Pdf

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· 73 ratings · 13 reviews

Start your review of The Mathematical Mechanic: Using Physical Reasoning to Solve Problems

A book full of insights about the interplay of mathematics and physics, or, more precisely, about how reasonings based on elementary principles of balances of forces, conservation of energy, and the like, can provide illuminating arguments (almost rigorous proofs, really) of a very large number of mathematical results of very different natures, some geometric, some algebraic, some analytic. Some of them are really impressively elegant: such as the "fish tank" proof of the Pythagorean theorem, ba A book full of insights about the interplay of mathematics and physics, or, more precisely, about how reasonings based on elementary principles of balances of forces, conservation of energy, and the like, can provide illuminating arguments (almost rigorous proofs, really) of a very large number of mathematical results of very different natures, some geometric, some algebraic, some analytic. Some of them are really impressively elegant: such as the "fish tank" proof of the Pythagorean theorem, based on the obvious principle that if the water in a tank at rest is not disturbed it shall remain undisturbed... (pp. 9-11), the proof of the theorem on the polygon of least area circumscribed around a given convex set and its generalizations (pp. 34-40), the fastest descent problem (pp. 104-6), or the dual cones theorem and the Gauss-Bonnet formula via an ingenious mechanical "device". A very enjoyable and enlightening book! ...more

What a delightful book for introducing new ways of looking at mathematical problems. Many time more difficult, but sometimes shockingly easier, mechanical solutions bring the untenable world of mathematics into the physical thanks to the creativity of Mark Levi.

Apr 09, 2019 Robert rated it liked it

A super intriguing idea.

Unfortunately I didn't know enough physics to fully appreciate it.

A super intriguing idea.

Unfortunately I didn't know enough physics to fully appreciate it.

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Niente da fare. Riponevo molte speranze su questo libro, tanto che me l'ero preordinato sei mesi prima che uscisse l'edizione in brossura. Invece è stato una delusione... ma iniziamo dal principio.

L'idea di Mark Levi è semplice: invece che usare la matematica per dimostrare le proprietà fisiche, lui ha usato le proprietà fisiche per dimostrare le proposizioni matematici, a partire dal teorema di Pitagora in poi. Come scrivevo, l'idea non è male, ma purtroppo io devo avere un blocco mentale per quanto riguarda la fisica, e quindi leggevo quelle pagine e non capivo nulla (a parte che se devo usare tutti quei congegni senza attrito, quelle molle di lunghezza a riposo zero e via discorrendo, tanto vale che mi metta a parlare di circonferenze senza spessore, no?). A essere del tutto onesti, ci sono due capitoli che almeno per me hanno avuto un certo valore: quello sui problemi di massimo e minimo, con l'idea di costruire una serie di computer analogica per risolvere i vari problemi, e quello sull'elettricità, con la derivazione delle leggi fondamentali a partire da quelle dei fluidi incompressibili. Anche l'appendice finale mi potrebbe essere utile se solo dovessi fare un po' di fisica, ma per fortuna non è il caso...

Insomma, a me non è piaciuto. Magari a voi però sì.

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Apr 09, 2015 Yi Niu rated it it was ok

The concept is great - to solve math problems or proof theorems using physical reasoning. And some examples using mechanics are really good. Science centres use some of the examples too.
However, some so-called physical examples, are made to fit the theorem. The author might have covered this point in the introduction, but I just don't like doing things just for doing them. One such example is on Page 111, computing integral of sintdt from 0 to x with a pendulum. Any one knowing what these symbo The concept is great - to solve math problems or proof theorems using physical reasoning. And some examples using mechanics are really good. Science centres use some of the examples too.
However, some so-called physical examples, are made to fit the theorem. The author might have covered this point in the introduction, but I just don't like doing things just for doing them. One such example is on Page 111, computing integral of sintdt from 0 to x with a pendulum. Any one knowing what these symbols mean should be able calculate this in less than 30 seconds, if they are fluent; otherwise, I don't think they would bother.
Some examples are never intuitive to me or rather, they might sound intuitive, but really rigorous mathematical proofs before I would admit it. One such example is on Page 78, and the author does address my comments here.
This book was recommended or referenced by one of youtube channels or the blogs I follow and subscribe, including but limited to ASAP Science, CGP Grey, MinuteEarth, minutephysics, SmarterEveryDay, Veritasium, Vsauce, WonderWhy, Matrix67(blog).
This one was probably referenced by Veritasium. ...more

Sep 14, 2010 Joe rated it it was ok

My assumption going into this book was that the author would use physical reasoning to make higher mathematical concepts clearer and more accessible. It's a great idea: Gauss' Law in 2D can be imagined as a spreading puddle of oil, of course!

Instead you get a mess of contrived analogies that are literary Rube Goldberg devices at best and not applicable at worst. The author would spend pages upon pages setting up these exercises and, though some were well done (like where to park in a drive-in to

What really killed me though was that after each hypothetical mechanical system was laboriously hammered together to elucidate some rather simple math concept, the author would provide a more rigorous mathematical proof which was always so much more valuable than the brittle physical analogies.

All in all, it's an interesting idea and a book worth borrowing from the library.

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Nov 04, 2014 Denise rated it liked it

What I took the time to understand, I really liked. My husband uses math for work on a daily basis, in fact, he was a math major in college. He was talking to a fellow math enthusiast and this book was mentioned. It sounded really interesting so I purchased a copy. Now, during my college years I did manage to make it through Geometry, Trig, and Calculus so even if I had to dust away a lot of cobwebs, I understood basically what the author was presenting. I like the physical reasoning because I'm What I took the time to understand, I really liked. My husband uses math for work on a daily basis, in fact, he was a math major in college. He was talking to a fellow math enthusiast and this book was mentioned. It sounded really interesting so I purchased a copy. Now, during my college years I did manage to make it through Geometry, Trig, and Calculus so even if I had to dust away a lot of cobwebs, I understood basically what the author was presenting. I like the physical reasoning because I'm a highly visual person and thinking about how fish tanks on poles can link to Pythagorean Theorem is pretty cool. Unfortunately, during the last decade, I've lost so much that trying to get through each section became a hefty undertaking. I've put the book back on my to-read shelf and hope to get through the rest of it at a later date. ...more

A delightful tour through various fields of math. Levi develops intuitive explanations for mathematical concepts by performing thought experiements. The theme that draws the book together is that the experiments rely on the reader's familiarity with real-world objects such as springs and fish tanks. The book does not focus on generalizable problem-solving techniques, so it wasn't especially helpful to me for use in class. But I found it fun that you can use a fishtank to demonstrate the Pythagor A delightful tour through various fields of math. Levi develops intuitive explanations for mathematical concepts by performing thought experiements. The theme that draws the book together is that the experiments rely on the reader's familiarity with real-world objects such as springs and fish tanks. The book does not focus on generalizable problem-solving techniques, so it wasn't especially helpful to me for use in class. But I found it fun that you can use a fishtank to demonstrate the Pythagorean theorem. ...more

Aug 19, 2013 Mario E. rated it did not like it

It was really bad. The concepts were not for the novice to physics or math. I was expecting it to be as clear as Stephen Hawkings books on astrophysics. But....