''The Penguin Dictionary of Curious and Interesting Numbers'' is a

reference book A reference work is a work, such as a paper, book or periodical (or their electronic equivalents), to which one can refer for information. The information is intended to be found quickly when needed. Such works are usually ''referred'' to ...

for

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

and

elementary number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathe ...

written by David Wells. The first edition was published in paperback by

Penguin Books Penguin Books is a British publishing, publishing house. It was co-founded in 1935 by Allen Lane with his brothers Richard and John, as a line of the publishers The Bodley Head, only becoming a separate company the following year.−1 In mathematics, −1 (also known as negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less t ...

and ''i''. The book includes some

irrational number In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two inte ...

s below 10 but concentrates on

integers An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

, and has an entry for every integer up to 42. The final entry is for

Graham's number Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which ...

. In addition to the dictionary itself, the book includes a

list of mathematicians Lists of mathematicians cover notable mathematicians by nationality, ethnicity, religion, profession and other characteristics. Alphabetical lists are also available (see table to the right). Lists by nationality, ethnicity or religion * Li ...

in chronological sequence (all born before 1890), a short

glossary A glossary (from grc, γλῶσσα, ''glossa''; language, speech, wording) also known as a vocabulary or clavis, is an alphabetical list of terms in a particular domain of knowledge with the definitions for those terms. Traditionally, a gl ...

, and a brief

bibliography Bibliography (from and ), as a discipline, is traditionally the academic study of books as physical, cultural objects; in this sense, it is also known as bibliology (from ). English author and bibliographer John Carter describes ''bibliography ...

. The back of the book contains eight short tables "for the benefit of readers who cannot wait to look for their own patterns and properties", including lists of polygonal numbers,

Fibonacci number In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

factorial In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \ ...

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...

s of primes,

factor Factor, a Latin word meaning "who/which acts", may refer to: Commerce * Factor (agent), a person who acts for, notably a mercantile and colonial agent * Factor (Scotland), a person or firm managing a Scottish estate * Factors of production, suc ...

s of

repunit In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book ''Recreat ...

s, and lastly the

prime factorization In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are s ...

and the values of the functions ''φ''(''n''), ''d''(''n'') and ''σ''(''n'') for the first hundred integers. The book concludes with a conventional,

alphabetical Alphabetical order is a system whereby character strings are placed in order based on the position of the characters in the conventional ordering of an alphabet. It is one of the methods of collation. In mathematics, a lexicographical order is t ...

index Index (or its plural form indices) may refer to: Arts, entertainment, and media Fictional entities * Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index'' * The Index, an item on a Halo megastru ...

Reviews

In a review of several books in The ''

College Mathematics Journal The ''College Mathematics Journal'' is an expository magazine aimed at teachers of college mathematics, particular those teaching the first two years. It is published by Taylor & Francis on behalf of the Mathematical Association of America and is ...

'', Brian Blank described it as "a charming and interesting book", and the ''

Chicago Tribune The ''Chicago Tribune'' is a daily newspaper based in Chicago, Illinois, United States, owned by Tribune Publishing. Founded in 1847, and formerly self-styled as the "World's Greatest Newspaper" (a slogan for which WGN radio and television ar ...

'' described the revised edition as "a fascinating book on all things numerical". By contrast, Christopher Hirst called it "a volume which none but propeller-heads will find either curious or interesting" in a review of another book in ''

The Independent ''The Independent'' is a British online newspaper. It was established in 1986 as a national morning printed paper. Nicknamed the ''Indy'', it began as a broadsheet and changed to tabloid format in 2003. The last printed edition was publish ...

''.

Style

Beside the serious mathematics and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

, Wells occasionally makes humorous or playful comments on the numbers he is discussing. For example, his entry for the number 39 largely consists of a joke involving the

interesting number paradox The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The " proof" is by cont ...

: :39 :This appears to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number to have the property of being uninteresting. :It is therefore also the first number to be simultaneously interesting and uninteresting. (pg. 120)

References

{{DEFAULTSORT:Penguin Dictionary of Curious and Interesting Numbers Mathematics books 1986 books Penguin Books books

Reviews

Style

See also

References