The Book of Numbers by John H. Conway (PDF)

Description

…the great feature of the book is that anyone can read it without excessive head scratching…You’ll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow. -IAN STEWART, NEW SCIENTIST”…a delightful look at numbers and their roles in everything from language to flowers to the imagination.” -SCIENCE NEWS”…a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible.” -WISCONSIN BOOKWATCH”This popularization of number theory looks like another classic.” -LIBRARY JOURNAL

User’s Reviews

Editorial Reviews: Amazon.com Review The Book of Numbers lets readers of all levels of mathematical sophistication (or lack thereof) understand the origins, patterns, and interrelationships of different numbers. Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The diagrams and pictures, many of which are in color, make this book particularly appealing and fun. A few of the discussions may be confusing to those who are not adept mathematicians; those who are may be irked that certain facts are mentioned without an accompanying proof. Nonetheless, The Book of Numbers will succeed in infecting any reader with an enthusiasm for numbers. From Library Journal The authors are well known to both academic and recreational mathematicians?Conway for inventing the “game of life” and discovering surreal numbers and Guy as the editor of the “Unsolved Problems” section in American Mathematical Monthly. They also coauthored the classic Winning Ways for Your Mathematical Plays (Academic, 1982). This popularization of number theory looks like another classic. Though number theory does not lend itself to fun and games, the authors take such joy in the order and patterns of numbers that you can’t help being fascinated by what is actually a fairly difficult subject. A combination of clear verbal explanations, wonderfully clever diagrams, and equations (for the real mathematicians) make sometimes complicated numerical concepts accessible to those “without particular mathematical background” (i.e., who are not at least graduate students in mathematics). The material is simplified but not dumbed down. A bridge to understanding and appreciating higher mathematical concepts, this book could appeal to anyone from a mathematically sophisticated high school student to a university mathematics professor.?Amy Brunvand, Univ. of Utah Lib., Salt Lake CityCopyright 1996 Reed Business Information, Inc. Review From the reviews:”This is a really fascinating book either to read or to browse in, or for reference – there is a good index, and I can strongly recommend it – it should be in every school and college library!” The Mathematical Gazette”… A delightful look at numbers and their roles in everything from language to flowers to the imagination.” Science News”… The great feature of the book is that anyone can read it without excessive head scratching … You’ll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow.” New Scientist From the Back Cover In The Book of Numbers, two famous mathematicians fascinated by beautiful and intriguing number patterns share their insights and discoveries with each other and with readers. John Conway is the showman, master of mathematical games and flamboyant presentations; Richard Guy is the encyclopedist, always on top of problems waiting to be solved. Together they show us why patterns and properties of numbers have captivated mathematicians and non-mathematicians alike for centuries. The Book of Numbers features Conway and Guy’s favorite stories about all the kinds of numbers any of us is likely to encounter, and many others besides. “Our aim”, the authors write, “is to bring to the inquisitive reader…an explanation of the many ways the word ‘number’ is used”. They explore patterns that emerge in arithmetic, algebra, and geometry, describe these patterns’ relevance both inside and outside mathematics, and introduce the strange worlds of complex, transcendental, and surreal numbers. This unique book brings together facts, pictures and stories about numbers in a way that no one but an extraordinarily talented pair of mathematicians and writers could do. About the Author John Horton Conway is the John von Neumann Professor of Mathematics at Princeton University. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Conway and Guy start this book with an enticing survey of how numbers pervade the English language, showing the hidden (or not-so-hidden) numerical roots of common words. They also mention other numbering systems, including the Roman numerals, Greek, Egyptian, and cuneiform Babylonian – numbers that persist in our 60-based measures of minutes and seconds, in both time and angle.Next, they move into squares, triangular numbers, and many others with rich geometric meanings. Chapters 1 and 2, especially, create vivid images that bring many of their concepts to life. I had a bit of trouble finding ch.3’s focus. It touches briefly combinatorics, a world in itself, and difference techniques. I found “Jackson’s Fan” fascinating, but too terse for easy application to real problems. After this, the going gets a lot tougher, fast.By ch 4, “Famous Families,” the illustration is no longer as vivid as before. Ch. 6, on fractions and decimal expansions also held some interest – it touches on complexity in the decimal forms of fractions, and the numeric roots from which it springs. The section on continued fractions is only just enough to titillate without really enlightening. Discussion of imaginary numbers is OK, and offers some enjoyable insights. The section on quaternions, though, does a lot less to invite personal involvement and stir the imagination. Later sections of the book present readable surveys of their topics, but require a lot more form the reader in the way of determination and mathematical background.If the whole book sustained the initial energy, it would have been an instant classic. The later parts of the book were clear, readable, and even enjoyable, but didn’t match the breadth or vividness of the first half. I enjoyed this, but I may not come back to it.//wiredweird

⭐This is an amazing book. A marvel in my humble oppinion!. I continuously get it in public or private libraries. This book is printed by Copernicus, and inprint of Springer-Verlang. Normally, this book is with perfect cover. All the editions in library are using Hardcover or Case bound: “Standard binding used for hardcover books. Several different types to choose from, but typically involves inside pages being sewn together in sections. These are then glued to end papers which are glued to covers spine..” Then, now I decided to buy this book in hardcover(case bound), in order to have this marble in my personal library.My surprise is this book is using a low quality cover named Tape Bound, a low price type of cover. Is there any difference? yes! the future of the book is compromised, because this case can break due the lack of flexibility. On the other side, this low quality case do not have a good affordance, as for example, to read the book while standing up.Quality of paper for the pages of the book is compromised too: the current edition is using traditional photocopy paper bound that affects the resolution and quality of letters, while the original/traditional editions in public and private libraries are in high quality paper.I feel like I received a copy of a book made in illegal places for photocopies. I feel I do not received and original copy.I attached a photo of the original binding compared with the binding this seller send to me.

⭐The sections at the beginning of the book are a sheer delight. I particularly enjoyed the chapter on figurative numbers, which shows how to get sums of powers of numbers by arranging them in geometric patterns. The idea of arranging the sum of sequential numbers into a triangular shape goes back to ancient times, but I suspect that some of the other arrangements are due to Conway and Guy. There is a really nice treatment of sums of cubes. Did you know that the sum of the entries in a multiplication table from, say 1 to 9, is the sum of the cubes 1^3 + 2^3 + … +9^3? I also enjoyed the section later on in the book on Catalan numbers.After the first two or three chapters, the book does seem rushed and there is much that I could not follow. I was especially frustrated by the method used to count the number of regions determined by the diagonals of a polynomial. It looks like a simple and original treatment of a classical problem, but after several attempts I just can’t follow the logic.

⭐We are in 1995, Conway is showing off numbers. Many of them. He warms us up pointing out that civilization has been using numbers everywhere and there are a bunch of composed words out there. And it took a great intellectual leap to see numbers as abstract entities. Then the numbers zoo broke loose. Many clever people started to create recipes for sequences of numbers. The fun here comes from the relations among numbers and geometric forms. Conway very often explains these relations using geometric isomorphisms making this book imaginary, transcendental, surreal, infinite, fun!

⭐I own a lot of books on Mathematics and Mathematical topics. This book truly is my favorite. The color illustrations, the other drawings and diagrams make the topics very understandable and tantalizing. The section on infinite and infinitesimal numbers alone, has inspired me to submit a paper on this subject to a Mathematics Journal. This book will cause anyone who is not already a Mathphile, to quikly become one. Take a look at the middle numbers in Pascals Triangle….with a little manipulation of this sequence, you produce CATALAN NUMBERS, which further leads to a number of interesting problems with Friezes and Polygons, none of which are mind bending in their demand of your mental powers. The chapters are all short, and you can open the book at random and find something very nice to dine on. BUY THIS ONE! Dr.Pratt.

⭐This is a great reference book.

⭐This is one of my favorite MATH books, the ideas from which I use for children, teachers, and friends in addition to personal entertainment. It is not just about numbers; it is about many aspects of real math. I so love it that I got two copies, one at home, the other at work. Prof. Conway is “a genius at work!” (book title about his love of math and life).

⭐This book is written at a level someone with a high school- / secondary school-level education in mathematics would find extremely accessible, but touches on topics that go beyond that or fill out gaps that the reader might not even know existed in their mathematical knowledge. From precisely where the mouse was as it ran up the clock to how cannonballs stack or how there are more infinities than you can count, there’s something in here for almost anyone who is mathematically inclined.

⭐Ich habe das Buch 1998 zufällig in einem Buchladen in London gesehen und erstanden. Im Gegensatz zu vielen langweiligen Deutschen Machwerken ist es mit vielen farbigen Darstellungen versehen und dennoch nicht Oberflächlich.Über Primzahlen steht viel mehr drinnen. Es ist eine Perle der Mathematik, die Pflicht sein sollte für Schüler, und die in einer Sammlung von Mathematikbüchern nicht fehlen sollte.Leicht verdaulicher Stoff, für denjenigen, der sich der Mathematik nicht versperrt.

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⭐Il libro ha pienamente soddisfatto le mie aspettative. La trattazione è progressiva, a partire da argomenti semplici a quelli più complessi e ciascun capitolo conclude stimolando approfondimenti individuali. È un’ottima base per affrontare testi più complessi. La maggior parte dei capitoli può essere affrontata con una preparazione di scuola media superiore, conoscenze a livello universitario possono essere utili per comprendere meglio alcuni argomenti ad esempio i numeri complessi. Peccato non sia più disponibile in lingua italiana, ma una conoscenza scolastica dell’inglese può essere sufficiente per la sua lettura

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⭐The quality of the book was in top condition and the content is unparallel. Every budding mathematician should own this one, this book is a rare gem brought about by two of finest mathematician of their time.

⭐Uno dei migliori testi del genere, con un contenuto informatico in alcune parti formidabile e con molti spunti per proseguire le ricerche.

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