» Q.E.D.: Beauty in Mathematical Proof (Wooden Books)

Q.E.D.: Beauty in Mathematical Proof (Wooden Books) Reviews

Customer Rating:
Summary: Twenty-three smple "proofs" of fundamental mathematical principles
Comment: Q. E. D. is an abbreviation for the Latin phrase "Quod erat demonstrandum", which means, "what had to be proved." In this book, Polster demonstrates 23 simple "proofs" of fundamental mathematical principles. I enclose the word proof in quotes because they are not always rigorous in the mathematical sense. In some cases they are more in the area of reasonably convincing reasoning.
Some examples are:

*) Cavalieri's principle
*Archimedes' theorem
*) The infinitude of primes
*) The divergence of the harmonic series
*) Slicing a cone by a plane will always give an ellipse
*) Formulas for the sums of the first n-th powers.

The mathematics is not rigorous, but that is not the intent here. The goal was to give a brief presentation and argument in favor of several fundamental mathematical principles. In my opinion, the author has found the mark, explaining these principles using language within the bounds of the merely interested rather than the learned professional.

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Customer Rating:
Summary: I want more!!!
Comment: If you feel that you have lost the touch of history of mathematics, have lost your creativity into the rigour of formal methods, and need integral calculus to solve simplest of the mathematical problems, this is the book you need.

Q.E.D. is a compilation of ancient mathematical problems with unexpectedly short mathematical proofs, which one you know them, are as simple as they can be, yet you may not think of them by yourself.

My idea is to train (or re-train) my mind with that creative thought with which you can find elegant proofs to mathematical problems rather than resorting to differential equations at each point. This book is just great on that.

I could work myself through half of the book in about two days. So thought-provoking is the content that I ended up proving a few theorems myself that were not included in the book. (Yet I see a simpler proof of one of them later in the book!)

I wish this book included five times more material than what it has. I wish to have all of mathematics to be taught in this fashion. Had once encountered a problem from electromagnetism that I could not even start on, finally gave up and continued reading the Feynman lectures on Physics (vol 2) to see the proof. The proof, albeit more complicated than all proofs in this book, Q.E.D., was still unexpectedly simpler.

I wish for a book like Q.E.D. that teaches me a lot more mathematics. But this is not to say that Q.E.D. hasn't served the purpose it aimed for.

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Customer Rating:
Summary: Reveals the simplicity which is mathematics.
Comment: I only submit this review in order to correct some of the other reviews. Apparently some folks don't accept that 1 = .9999...

The proof is simple. Let x = .9999...

Therefore, 10x = 9.9999... and x= .99999 and so, 10x - x = 9x. That is, 9.9999... - .9999... = 9.0000 (.9999... - .9999... = 0000...). That is, 9x = 9.0000. Hence, x = 1.000 since 9/9 = 1.

Why does the mathematical operators allow the results to crank out 1 = .9999....? Because the "=" sign operates as an association of two different mathematical models in the sense 1 is a mathematical model for .9999... just as .9999... is a mathematical for 1. It was this thinking that led Descartes to assert y = mx + b whereby this equation constitutes a mathematical model of the line in algebra just as the line is a mathematical model of y = mx + b in geometry. All proofs involve mathematical models. Goedel numbers are models of theorems. See J. N. Crossley's little book or D'Abro's book on the rise of physics (volume one) for lucid explanations of mathematical modeling.

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Customer Rating:
Summary: Beautiful mathematics brought alive
Comment: Great little book! Mathematicians will often tell you that mathematics is beautiful. However, they usually have a hard time conveying the beauty of math to their nonmathematical friends. The author/illustrator has done a great job in capturing this beauty in the form of truly magnificent illustrations of proofs, making Q.E.D. the ideal read for anybody interested in discovering this elusive mathematical beauty for themselves.

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Customer Rating:
Summary: Seeing is believing
Comment: I like just about everything about this little book. There are a couple of other books on pictorial proofs out there (The Most Beautiful Mathematical Formulas by Salem et. al. and Proofs without Words by Nelson), but this one is by far the most visually appealing. I particularly like the beautiful etching-like illustrations which, in my opinion, capture the timeless beauty of the various proofs very well.

Included in the book is a nice mix of well-known and not so well-known material. For example, many people will know the nifty pizza proof that relates the circumference of the circle with its area, but it is probably quite a pleasant surprise for many that a similar relationship exists between the surface of a sphere and its volume.

B.t.w., and if you have also read the other reviews this may surprise you, I really did read most of the book.

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