Customer Reviews

Archimedes' Revenge

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4 star:		(1)
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2 star:		(1)
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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.

This book might always have come across as a disjointed read (as it delves into four separate areas of mathematics) but it also suffers because these areas fail to hold the reader's attention. The four sections covered are number theory, shapes and topology, computer science, and the mathematics of voting.

Of the four, the number theory section is the most interesting, but a more in-depth and charming analysis of this area of mathematics can be found in Simon Singh's two books: Fermat's Last Theorem and The Code Book.

The chapter on computing machines is weakened by the fact that the book was published first in 1989 and consequently is rather dated.

Overall I would describe this book as a page-turner but only in the sense that I skipped pages to swiftly conclude certain chapters.

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.

I found the book to be rather interesting, and not difficult to understand. A scientific or mathematical background is an added plus while reading the book. I felt that it got bogged down in some sections, but they were of little interest to me and skipping them did not hinder the overall effect of the book. Enjoyable light reading, for if you ever thought,"What the hell is math good for?". Good section on cryptology.

Hoffman was very readable, especially the section on number theory. Only the last few chapters on game theory got bogged down in the technicalities.

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".

You may have thought math was cut and dry. This book blows that thought away. In easy to understand, lay language, this book explains some of the wierdness in mathematics. A must read for computer science people.

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.

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.