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Albert H. Beiler
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Recreations in the Theory of Numbers (Dover Math Games & Puzzles) 2nd Revised ed. Edition

by Albert H. Beiler (Author)
4.7 4.7 out of 5 stars 31 ratings
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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.

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  1. ISBN-10
    0486210960
  2. ISBN-13
    978-0486210964
  3. Edition
    2nd Revised ed.
  4. Publisher
    Dover Publications
  5. Publication date
    June 1, 1964
  6. Language
    English
  7. Dimensions
    5.4 x 0.78 x 8.5 inches
  8. Print length
    368 pages
  9. See all details
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Product details

  • Publisher ‏ : ‎ Dover Publications; 2nd Revised ed. edition (June 1, 1964)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 368 pages
  • ISBN-10 ‏ : ‎ 0486210960
  • ISBN-13 ‏ : ‎ 978-0486210964
  • Item Weight ‏ : ‎ 14.6 ounces
  • Dimensions ‏ : ‎ 5.4 x 0.78 x 8.5 inches
  • Customer Reviews:
    4.7 4.7 out of 5 stars 31 ratings

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Albert H. Beiler

Albert H. Beiler

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Customer reviews

4.7 out of 5 stars
4.7 out of 5
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31 global ratings

Top reviews from the United States

Peter McGowan
5.0 out of 5 stars Highly addictive!
Reviewed in the United States on June 11, 2014
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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!
13 people found this helpful
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Amazon Customer
5.0 out of 5 stars Serious Fun With Number Theory
Reviewed in the United States on June 22, 2016
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An excellent book for anyone who enjoys fooling around with numbers. I mainly used it for programming a HP50g to solve Pell's equations, as well as other fun programs, i.e.,finding all pairs of squares which sum up to a given number (for example the hp50g takes about 25 seconds to find the 8 pairs of squares that sum up to 8,724,165,747,570, once you write the program. Has chapter with challenging problems, although you will need to spend quite some time reading the book (and understand what you are reading)!
6 people found this helpful
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Steve
4.0 out of 5 stars Great introduction to number theory
Reviewed in the United States on January 2, 2015
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Great introduction to number theory...always wondered how they figured out this kind of stuff. Surprisingly readable for it's content.
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Michael
5.0 out of 5 stars Very interesting -- May be a difficult read for a high school math student
Reviewed in the United States on March 28, 2014
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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.
7 people found this helpful
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Andrew S.
5.0 out of 5 stars Wouldn't recommend it to someone who is new to number theory
Reviewed in the United States on April 9, 2018
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Hard to comprehend. Sometimes I had to read the same paragraph multiple times in order to understand the logical process. Wouldn't recommend it to someone who is new to number theory.
2 people found this helpful
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Maarten Daams
5.0 out of 5 stars Excellent for a numbers geek
Reviewed in the United States on May 18, 2014
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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.
One person found this helpful
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OldFish
5.0 out of 5 stars Excellent and Fun
Reviewed in the United States on March 21, 2018
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Replacing a copy that is falling apart.
One person found this helpful
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G. Player
3.0 out of 5 stars kind of dated, but still fun
Reviewed in the United States on January 27, 2015
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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
2 people found this helpful
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Virginia S
5.0 out of 5 stars Really good book- for very smart math people :D
Reviewed in Canada on August 6, 2019
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Highly recommended for people who love math and all things related to math! It's a nice thick book, high quality and made for the smart person who adores solving complex riddles.
Truthfully, this was a gift for my husband and he adores it. He's very into the sciences and he patiently explains the book to me and why he's laughing in delight while I do my best to 'get it'. It was part of our marriage vows that math and physics wouldn't be talked about before my morning coffee and other than that I'm happy to learn lol!
It's a really cool book and if I get my wind up, I'll give it a read, but for now it gives my hubby hours of delight. If you have 'that person' in your life, buy them this book and try to learn a bit from it while you do, you'll both be better for it :)
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seb b
5.0 out of 5 stars Very good overall
Reviewed in the United Kingdom on April 29, 2019
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As described. Arrived slightly early.
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Luigi Morelli
5.0 out of 5 stars Tht's what I was looking for!
Reviewed in Italy on July 25, 2013
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I was interested in Number Theory since I was a child, producing programs on my Commodore 64.
Books that I have bought were related either to automatic calculus (Concrete mathematics by Knuth, Prime Numbers by Crandall and Pomerance) or to abstract number theory. This book is instead related to problems and problem solving, with numerical examples and the theory behind them restricted to the problem. The Author also gives hints on how to enhance the search, offering heuristics and optimization ideas.
All in all, a wonderful book to learn computing techniques focusing the study to the actual subject.
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Grizonnet
5.0 out of 5 stars Excellent
Reviewed in France on May 10, 2012
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Fabuleux livre pour les amoureux de l'arithmétique, ou même les simples curieux.
Un bagage niveau DEUG permet d'apprécier les trésors contenus dans ce livre.
A noter qu'il est en anglais et que l'auteur semble avoir beaucoup d'humour, certains passages sont délicats à traduire mais rien d'insurmontable.
On y retrouve beaucoup de grands classiques mais surtout des curiosités originales et bien amenées. Comme beaucoup de livre de ce genre, il ne se veut pas comme un manuel de mathématiques académique et donc certains passage vous demanderont de démontrer vous-même les blancs d'une affirmation à l'autre. Ou alors de vous laisser porter par le propos de l'auteur pour accéder à des résultats intéressants.
C'est donc une lecture très stimulante et instructive.
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Peter Van Eetvelt
5.0 out of 5 stars Five Stars
Reviewed in the United Kingdom on September 29, 2015
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EXCELLENT
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