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Comment: Condition: Very good condition., Clean - No marks of any kind. / Binding: Trade Paperback / Publisher: Dover Publications / Pub. Date: 1964 Attributes: 349p / Stock#: Z992175330 () * * *This item qualifies for FREE SHIPPING and Amazon Prime programs! * * *

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Recreations in the Theory of Numbers (Dover Recreational Math) Paperback – June 1, 1964

by Albert H. Beiler (Author)

15 customer reviews

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Number theory, the Queen of Mathematics, is an almost purely theoretical science. Yet it can be the source of endlessly intriguing puzzle problems, as this remarkable book demonstrates. This is the first book to deal exclusively with the recreational aspects of the subject and it is certain to be a delightful surprise to all devotees of the mathematical puzzle, from the rawest beginner to the most practiced expert. Almost every aspect of the theory of numbers that could conceivably be of interest to the layman is dealt with, all from the recreational point of view. Readers will become acquainted with divisors, perfect numbers, the ingenious invention of congruences by Gauss, scales of notation, endless decimals, Pythagorean triangles (there is a list of the first 100 with consecutive legs; the 100th has a leg of 77 digits), oddities about squares, methods of factoring, mysteries of prime numbers, Gauss's Golden Theorem, polygonal and pyramidal numbers, the Pell Equation, the unsolved Last Theorem of Fermat, and many other aspects of number theory, simply by learning how to work with them in solving hundreds of mathematical puzzle problems. The text is extremely clear and easy to follow, and it bears convincing evidence of the author's deep sense of humor and his outstanding ability to lure the reader through even the most difficult trails by skillfully revealing their fascination. The problems distributed throughout the book are explained in the final chapter and there is also a supplementary chapter containing 100 problems and their solutions, many original. There are over 100 tables.
The appeal of these stimulating puzzles lies in their ready comprehensibility and the fact that only high school math is needed to master the fundamental theory presented by the author. This theory is itself interesting and of use to the more serious math student, but it may be omitted by lay readers without diminishing the book's challenge or detracting from the pleasure-giving nuggets it contains.

Recreations in the Theory of Numbers (Dover Recreational Math)

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Product Details

Series: Dover Recreational Math
Paperback: 368 pages
Publisher: Dover Publications; 2nd Revised edition edition (June 1, 1964)
Language: English
ISBN-10: 0486210960
ISBN-13: 978-0486210964
Product Dimensions: 0.8 x 5.5 x 8.5 inches
Shipping Weight: 12 ounces (View shipping rates and policies)
Average Customer Review: 4.5 out of 5 stars See all reviews (15 customer reviews)
Amazon Best Sellers Rank: #266,413 in Books (See Top 100 in Books)
- #69 in Books > Science & Math > Mathematics > Pure Mathematics > Number Theory
- #759 in Books > Humor & Entertainment > Puzzles & Games > Puzzles

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Customer Reviews

4.5 out of 5 stars

5 star		67%
4 star		20%
3 star		13%
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Most Helpful Customer Reviews

30 of 31 people found the following review helpful

Lots of examples, lots of tables, lots of fun

By D. Taylor on December 26, 2000

Format: Paperback

This book was my first exposure to Number Theory, coming from an engineering background. This book got me hooked. You could almost say the book takes an engineering approach to number theory: Lots of examples, lots of tables but not a lot of rigorous, long proofs. This book is set apart from most textbooks by those facts. You won't find such extensive examples and tables in any textbook (and I have about 50+ texts on Number Theory). Conversly, no self-respesting professor could present so many results without proof. But that's the fun of this book. I recommend this book over "An Adventures Guide to Number Theory" by Richard Friedberg for uninitiated.

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19 of 19 people found the following review helpful

Recreational Mathematics Is Not A Contradiction In Terms

By Henry M. Dobb on March 30, 2002

Format: Paperback

If you are curious about numbers (as I am), this is one of several books you need to have in your library. It is informative, entertaining, comprehensive and easy to read, even if you are not blessed with a mathematics degree from an institution of higher learning.
This book is well-organized, beginning with topics that are easy to grasp, then going on to more complicated ideas. The contents include such terms as prime numbers, perfect numbers, amicable pairs, sociable numbers, divisors, congruences, cyclical numbers, repunits (a term the author coined) and logarithms. The book reveals many curiosities about common artcles such as squares, triangles and circles. More complex topics such as a resolution of a number into prime factors and Pell equalities are shown in a manner that is informative and easy to comprehend. The grand climax of the book is a stirring discussion of Fermat's Last Theorem.
This volume remains a 'good read' despite the fact that it is almost forty years old. Although much of what it in this book has been superceded over the course of time, this boof is not obsolete. If you have any interest in numbers, buy this book if you do not already possess a copy of it.

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17 of 17 people found the following review helpful

The best writing in the field

By A Customer on January 5, 1999

Format: Paperback

For one reason or another, this book contains the clearest exposition of Mersenne primes and quadratic residues I have ever read. It is very heavy on results and very light on proofs, so don't expect to learn anything here, but expect to be entertained.

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10 of 12 people found the following review helpful

Deep insights into Number Theory, Well Written, Often quoted

By Charlestonideas@hotmail.com on July 19, 1998

Format: Paperback

A classic in number theory and a great introduction for the newcomer. I use it in my research on Ancient Mathematics. Richard Brown, Research Director, 1248 Institute, Charleston, SC

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3 of 3 people found the following review helpful

Highly addictive!

By Peter McGowan on June 11, 2014

Format: Paperback Verified Purchase

I strongly advise against buying this book - it will waste hundreds of hours with fascinating patterns and absorbing connections that most never dreamed of! While requiring nothing more than middle high school mathematics, the text still contains quite advanced ideas - for example and simple proof that Format number that are prime are also the constructible number with ruler and compass. There are also superb discussions (in an entertaining way) of Farey series, primitive roots, Pellian numbers, Pythagorean triples, quadratic residues, prime number distribution and the zeta function, and on and on - never boring. Essential reading for budding numbers' men! The book is not new but it has stood the test of time and is still a masterpiece - one of the greatest time burners I have ever read!

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2 of 2 people found the following review helpful

Very interesting -- May be a difficult read for a high school math student

By Michael Gibb on March 28, 2014

Format: Paperback Verified Purchase

This book is extremely entertaining and shows the intriguing interplay between the different properties of numbers. I would recommend this book to anyone interested and proficient in mathematics. Even though the book states that it has a target audience of anyone who has completed high school mathematics, the depth and breadth of the analysis and theory presented in this book lends itself to a much more educated reader. I can not recommend this book highly enough.

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kind of dated, but still fun

By G. Player on January 26, 2015

Format: Paperback Verified Purchase

this book doesn't really stand up to modern books, in that it is just a little too dry... not enough explanation as to the "why" that these things work.
there aren't as many metaphors and mental exercises to help you wrap your head around all of the topics as you would expect if this were a modern book.
I have enjoyed reading it though

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Excellent for a numbers geek

By Amazon Customer on May 18, 2014

Format: Paperback Verified Purchase

This is a great book for everyone who loves to learn about the properties of numbers at times. Though somewhat difficult at times and a bit old-fashioned now, still a great book that I keep going back to time and again.

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Most Recent Customer Reviews

Interesting relationships of numbers

Haven't finished it yet - it's very good

Published 8 months ago by shelly

Great introduction to number theory

Great introduction to number theory...always wondered how they figured out this kind of stuff. Surprisingly readable for it's content.

Published 11 months ago by Steve

Five Stars

Item as described. Thank you.

Published 15 months ago by Nia

Full of info

...but poorly written. It's very interesting in a historical sense. For instance, Table 9 shows composite Mersenne's numbers up to n=251, most of them with question marks when a... Read more

Published on July 28, 2002 by Bobby R. Treat

Full of info, but poorly written.

And NOT written in a recreational style, by any means.

Published on July 27, 2002 by Bobby R. Treat

A classic

This is a great book for math amatuers like myself. Expertly written. Great introduction. Great examples. Read more

Published on March 9, 2002 by Nicolas Schmelzer

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