The Math Hidden Within ISBN Numbers

An ISBN (or  International Standard book Number) is a 13-digit number uniquely identifying books and “book-like” products. The number is used to differentiate one title, or edition of a title, from a specific publisher.  For example, an e-book and a paperback version of the same book would each have different ISBNs. Changing the cover of a book does not result in a new edition, since the text is the same.

Not all books have an ISBN number. If the book is printed privately and is not intended for bookstore or library distribution, then it does not need an ISBN number.

ISBN numbers were first derived in 1967 in the United Kingdom by David Whitaker, who based the system upon the 9-digit Standard Book Number (SBN) created in 1966. The 10-digit format was then developed the International Organization for Standardization (ISO) and published in 1970. Ironically, the UK continued to use the 9-digit ISBN code until 1974. Old SBNs were converted to ISBNs by adding a zero prefix. ISBNs remained 10-digits long until January 1, 2007, when ISBNs switched to a 13-digit format.

The number is divided into five parts of variable length, each separated by a hyphen: 

1. A Prefix (only applicable to 13-digit ISBNs). To date, only “978” or “979” have been used.
2. Identifier for national or geographic location of the publisher.
3. The publisher identifier.
4. The title identifier which differentiates a particular title or edition.

A check digit which validates the ISBN.

 For my fellow math geeks out there, the check digit for an ISBN-13 number is calculated via the following procedure:

• Multiply each of the preceding 12-digits by a 1 or a 3 (alternating, starting with 1)
• Sum all the products
• Divide the result by 10 and calculate the remainder (mod 10)
• Subtract the remainder from 10

  For the ISBN-13 number for Apricots and Wolfsbane: 978-1-946802-02-6, the check digit (6), is calculated:

When querying to find out the ISBN number of a book, If you make a mistake in writing the ISBN, the calculation result will give a number that cannot be divided by 10, and the book will not be found.

Math is everywhere...

Source :1

Hazal A. /Şehit Erhan Ar Vocational and Technical Anatolian High School