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

reference book A reference work is a document, such as a Academic publishing#Scholarly paper, paper, book or periodical literature, periodical (or their electronic publishing, electronic equivalents), to which one can refer for information. The information ...

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 is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for exampl ...

written by

David Wells David Lee Wells (born May 20, 1963) is an American former baseball pitcher who played 21 seasons in Major League Baseball (MLB) for nine teams, most notably the Toronto Blue Jays and New York Yankees. Nicknamed "Boomer", Wells was considered on ...

. The first edition was published in paperback by

Penguin Books Penguin Books Limited is a Germany, German-owned English 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 ...

in 1986 in the UK, and a revised edition appeared in 1997 ().

The entries are arranged in increasing order of magnitude, with the exception of the first entry on

−1 In mathematics, −1 (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 than 0. ...

and ''i''. The book includes some

irrational number In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, ...

s below 10 but concentrates on

integers An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

, and has an entry for every integer up to 42. The final entry is for Graham's number. In addition to the dictionary itself, the book includes a list of mathematicians in chronological sequence (all born before 1890), a short

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

, 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 ''bibliograph ...

. 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 number In mathematics, a polygonal number is a Integer, number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate numbers. Polygonal numbers were first studied during the 6th century BC by the Ancien ...

Fibonacci number In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...

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 (mathematics), 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 ...

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 (''decimal fractions'') of th ...

reciprocals of primes, factors of repunits, and lastly the

prime factorization In mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a comp ...

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 ...

index Index (: indexes or 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 the Halo Array in the ...

Reviews

In a review of several books in The '' College Mathematics Journal'', Brian Blank described it as "a charming and interesting book", and the ''

Chicago Tribune The ''Chicago Tribune'' is an American daily newspaper based in Chicago, Illinois, United States. Founded in 1847, it was formerly self-styled as the "World's Greatest Newspaper", a slogan from which its once integrated WGN (AM), WGN radio and ...

'' 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 publis ...

''.

Style

Beside the serious mathematics and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

, 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 contradi ...

: :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

Contents

Reviews

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References