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Archimedes' Revenge
Paul Hoffman

Ballantine Books, 1997 - 285 pages

average customer review:based on 8 reviews
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   highly recommended  highly recommended





Archemides Revenge by Paul Hoffman

This book is perfect for math buffs. The author discusses the
intricacies of dot patterns, prime numbers, codes, geometric
shapes, conic forms, states and the Palindrom check-just to
mention a few of the topics treated. Math majors would find this
work a delight. It is perfect for a school math project.
You could also develop a thesis from some of the challenges
proposed in this book. It is worth the price for persons
interested in higher mathematics and the sciences. It could be
useful for computer scientists and machine language specialists.


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An excellent source of material for anyone researching an essay in mathematics

Long on joy and short on perils, this book is full of mathematical excitement. The thirteen chapters, each of which could stand alone as a mathematical essay, describe some of the most fascinating problems in pure and applied mathematics. Although some of the problems have remained unsolved for centuries, the book is so well written that even someone who has never heard of the problem will have no trouble understanding it or the solution.
The first three chapters deal with number theory, and the accent is on the use and limitations of computers in solving problems. Emphasis is placed on the famous cattle problem of Archimedes, which is the source of the book's title. Chapter four deals with cryptography and explains some of the historical consequences of faulty codes. The famous Beale ciphers are explained in detail.
The large egg pictured on the cover is the topic of chapter five, with extensive forays into the tiling of surfaces. Of particular interest is the fact that the topic of the first paper of James Clerk Maxwell was the construction of true egg shapes. The computer solution of the famous four-color problem is covered in chapter seven, with new directions in the use of computer graphics cited.
Turing machines and NP complete problems along with the possibility of a combinatorial explosion are the topics of chapters eight, nine and ten. Particular emphasis is placed on the chess-playing computer. Chapters twelve and thirteen deal with the mathematical flaws in the search for a perfect democratic system. Whether contrived or from history, the examples are fascinating and at times counter-intuitive.
An excellent source of material for anyone researching an essay in mathematics, this book deserves a place in all libraries.



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Great for non-math types to see the wonder of math

Most people have math-phobia, which is too bad, because math exhibits a certain beauty and perfection. The great thing about Paul Hoffman's "Archimedes' Revenge" is that he shows you the beauty and perfection without your having to be a math major to understand.

Moreover, for anyone who's wondered what use math is, Hoffman can answer that as well. Among the subjects covered are: cryptology (code making and code breaking), architecture, computer science, and political science.

The book is divided into a number of sections, ranging from number theory to topology to game theory. While these may sound like esoteric (and useless) concepts, Hoffman masterfully weaves in stories, such as the (in)famous Beale cipher, a secretly coded treasure map that has resisted all attempts to crack it for over 100 years.

I recommended to a colleague of mine that she buy this book for her teenage son, who is bright but a slacker. She reported that he raved about the book and was so eager to discuss it with her!

As an example of the sort of thing covered in this book, Hoffman describes a game where A, B, and C all have balloons and darts. A hits his target 80% of the time; B hits his target 60% of the time; and C hits his target 40% of the time. If each person attacks his strongest opponent, who wins most often? Surprisingly, the answer is C, because A and B concentrate their attacks on each other.

In summary, if you have math-phobia but would like to conquer it, this is a great place to start. There are no equations to speak of, just concepts explained in (relatively) plain English. It may take a couple of readings to understand it all, but it's definitely within grasp for those who progressed no farther than Algebra 2 in high school.


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Very like a Martin Gardner book

Well written and the author anticipates current interest in number theory
and cryptography. It reminded me very much of the earlier Martin Gardner " Mathematical Magic Show".


reviews: page 1, 2



Now anyone can understand what the mathematical geniuses are thinking . . . .
* How topologists figured out the way to turn a smokestack into a bowling ball -- and why.
* How game theorists discovered that to elect the candidate of your choice you must sometimes vote for his opponent.
* How computer theorists intend to create a robot that will think for itself -- and do all the housework.
* How cryptographers have been laboring since 1822 to decipher a map that will lead to a buried treasure worth millions of dollars.
Archimedes' Revenge takes the reader on a guided tour of the world of contemporary mathematics and makes its infinite marvels comprehensible, relevant, and fun.
"A breezy and lighthearted account of a number of topics in and around the periphery of mathematics . . . Mr. Hoffman approaches mathematics as a storyteller, and a good one." -- The New York Times Book Review


From the Paperback edition.


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