New bookshelf entry: The Book of Numbers

After seeing John H. Conway and Richard Guy‘s
The Book of Numbers cited in yet another interesting article/book/whatever, I finally decided that I clearly had to read it. (It seems to get cited a lot in certain circles.) I wasn’t disappointed — it’s a fun, well-written, and far-ranging tour of mathematical ideas all stemming from the concept of number. You might think such a topic would be somewhat limiting, but you would be very wrong! Along the way Conway and Guy manage to touch on such topics as number theory, geometry, algebra, pi, fractions, partitions, Babylonians, infinity, irrationals, primes, pineapples, Fibonacci numbers, Pascal’s triangle, complex numbers, quaternions, surreal numbers, harmonic numbers… to name just a few.

In order to pack so much interesting stuff into the book, the presentation is by necessity fairly concise; for this reason and because of the topics covered, the level of the book is definitely more advanced than many of the other books on my bookshelf. The authors don’t shy away from advanced topics, but the writing style is still friendly and compelling. Even if you don’t understand everything in the book (even I didn’t follow a few things the first time), you’ll undoubtedly learn some cool things, and it could be a book to grow with as you continue to learn more mathematics.

At some point I hope to create a page with more detailed descriptions of all the books on my bookshelf (which can be found in the right margin). In the meantime, if you read a book that you think I should include, or read one of the books already on the bookshelf and want to talk about it or offer your opinion or comments, of course feel free to leave a comment or e-mail me.

[Note: isn’t paying me to link to them or anything, it’s just a convenient way for me to link to more info about the book. If you want to buy a copy, of course feel free to buy it from anywhere you want!]

About Brent

Associate Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
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3 Responses to New bookshelf entry: The Book of Numbers

  1. MJ DeYoung says:


    Coool site! I recently got a copy of “The Book of Numbers,” and have a question re Chap. 2.

    When the authors talk about “rows” and “sections” in the very first illustration, are they talking about “rows” in the traditional sense, i.e., lines read left to right, versus columns, top to bottom? I’m at work now, but I seem to recall counting 5 separate “sections” with varying numbers of columns. I think the first “section” starts with one column 0-9, the second “section two columns (01-09?) up to the fifth “section, with five columns? and I seem to recall there are something like 9 “rows” across the whole illustration, i.e. all 5 “sections” of illus 2-1.

    I’m at work right now, so don’t have the book in front of me; but I wanted to write you this quick question. When I get home I’ll be more specific as to what I am referencing. Suffice it to say that overall I think the book is very interesting, but I’m having a little trouble following their point in the very first illustration (I think its 2-1).

    I also think some of the organge/red colors of other illustrations didn’t come out quite clear, i.e. some illustraions look all red, when the authors are refering to a “checkerboard” pattern. However, I understand many other parts of the book. Any insight re this first part of Chap. 2 would be appreciated.

    MJ DeYoung

  2. Brent says:

    Hi MJ,

    The beginning of Chapter 2 is poorly worded, but yes, they are talking about rows in the traditional sense. When they say “writing the numbers in rows of 1, 2, 3” they mean “write out all the numbers using rows of length 1, then using rows of length 2, then using rows of length 3, …” and so on.

    If we write the numbers in rows of 3, for example, we get something like this:

    0 1 2
    3 4 5
    6 7 8
    9 10 11

    That is, we put the first three numbers in the first row, then the next three numbers in the second row, and so on. Each row has three numbers. This is, of course, the third “section” of figure 2.1. Does that help?

    I agree about the orange/red, it didn’t come out well in my copy either. If I stare very carefully at Figure 2.4 I can tell a slight difference between orange and red, but it’s a very poor choice of colors. The same goes for Figure 2.5.

  3. MJ DeYoung says:

    Hello Brent,

    “Does that help?” Yes! Thanks….Should they ever release another edition of this book, I would suggest to the publishers the following: 1. that they re-edit
    2. that they hire YOU for the job

    What’s wrong with these people? Don’t they realize that when they allow this kind of carelessness, they turn-off many reviewers/buyers – such as myself.

    Thanks Again,
    MJ DeYoung
    Boston, MA

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