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The Penguin Dictionary Of Curious And Interesting Numbers
''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 (). Contents The entries are arranged in increasing order of magnitude, with the exception of the first entry on −1 and ''i''. The book includes some irrational numbers below 10 but concentrates on integers, 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, and a brief 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 numbers, prime numbers, factorials, decimal r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults and inspiring their further study of the subject. The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics. Topics Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Ancient Greeks, who investigated and discussed properties of Pronic number, oblong, Triangular Number, triangular, and Square number, square numbers. Definition and examples The number 10 for example, can be arranged as a triangle (see triangular number): : But 10 cannot be arranged as a square (geometry), square. The number 9, on the other hand, can be (see square number): : Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number): : By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
College Mathematics Journal
The ''College Mathematics Journal'' is an expository magazine aimed at teachers of college mathematics, particularly those teaching the first two years. It is published by Taylor & Francis on behalf of the Mathematical Association of America and is a continuation of the ''Two-Year College Mathematics Journal''. It covers all aspects of mathematics. It publishes articles intended to enhance undergraduate instruction and classroom learning, including expository articles, short notes, problems, and "mathematical ephemera" such as fallacious proofs, quotations, cartoons, poetry, and humour. Paid circulation in 2008 was 9,000, and total circulation was 9,500. The MAA gives the George Pólya Awards annually "for articles of expository excellence" published in the ''College Mathematics Journal''. References External links *''The College Mathematics Journal''at JSTOR''The College Mathematics Journal''at Taylor & Francis Taylor & Francis Group is an international company orig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Index (publishing)
An index (: usually indexes, more rarely indices) is a list of words or phrases ('headings') and associated pointers ('locators') to where useful material relating to that heading can be found in a document or collection of documents. Examples are an index in the back matter of a book and an index that serves as a library catalog. An index differs from a word index, or Concordance (publishing), ''concordance'', in focusing on the subject of the text rather than the exact words in a text, and it differs from a table of contents because the index is ordered by subject, regardless of whether it is early or late in the book, while the listed items in a table of contents is placed in the same order as the book. In a traditional ''back-of-the-book index'', the headings will include names of people, places, events, and concepts selected as being relevant and of interest to a possible reader of the book. The indexer performing the selection may be the author, the editor, or a professional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alphabetical Order
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 the generalization of the alphabetical order to other data types, such as sequence (mathematics), sequences of numbers or other ordered mathematical objects. When applied to strings or sequence (mathematics), sequences that may contain digits, numbers or more elaborate types of elements, in addition to alphabetical characters, the alphabetical order is generally called a lexicographical order. To determine which of two strings of characters comes first when arranging in alphabetical order, their first letter (alphabet), letters are compared. If they differ, then the string whose first letter comes earlier in the alphabet comes before the other string. If the first letters are the same, then the second letters are compared, and so on. If a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor Function
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (including 1 and the number itself). It appears in a number of remarkable identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who gave a number of important congruences and identities; these are treated separately in the article Ramanujan's sum. A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function. Definition The sum of positive divisors function ''σ''''z''(''n''), for a real or complex number ''z'', is defined as the sum of the ''z''th powers of the positive divisors of ''n''. It can be expressed in sigma notation as :\sigma_z(n)=\sum_ d^z\,\! , where is shorthand fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
φ(n)
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In other words, it is the number of integers in the range for which the greatest common divisor is equal to 1. The integers of this form are sometimes referred to as totatives of . For example, the totatives of are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, since and . Therefore, . As another example, since for the only integer in the range from 1 to is 1 itself, and . Euler's totient function is a multiplicative function, meaning that if two numbers and are relatively prime, then . This function gives the order of the multiplicative group of integers modulo (the group of units of the ring \Z/n\Z). It is also used for defining the RS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 composite number, or it is not, in which case it is a prime number. For example, is a composite number because , but is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example . Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer using mental or pen-and-paper arithmetic, the simplest method is trial division: checking if the number is divisible by prime numbers , , , and so on, up to the square root of . For larger numbers, especially when using a computer, various more sophis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ''Recreations in the Theory of Numbers''. A repunit prime is a repunit that is also a prime number. Primes that are repunits in base-2 are Mersenne primes. As of October 2024, the largest known prime number , the largest probable prime ''R''8177207 and the largest elliptic curve primality-proven prime ''R''86453 are all repunits in various bases. Definition The base-''b'' repunits are defined as (this ''b'' can be either positive or negative) :R_n^\equiv 1 + b + b^2 + \cdots + b^ = \qquad\mbox, b, \ge2, n\ge1. Thus, the number ''R''''n''(''b'') consists of ''n'' copies of the digit 1 in base-''b'' representation. The first two repunits base-''b'' for ''n'' = 1 and ''n'' = 2 are :R_1^ 1 \qquad \text \qquad R_2^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a '' multiple'' of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer n is divisible by a nonzero integer m if there exists an integer k such that n=km. This is written as : m\mid n. This may be read as that m divides n, m is a divisor of n, m is a factor of n, or n is a multiple of m. If m does not divide n, then the notation is m\not\mid n. There are two conventions, distinguished by whether m is permitted to be zero: * With the convention without an additional constraint on m, m \mid 0 for every integer m. * With the convention that m be nonzero, m \mid 0 for every nonzero integer m. General Divisors can be negative as well as positive, although often the term is restricted to posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal (mathematics)
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yields the original number (since the product of the number and its reciprocal is 1). The term ''reciproca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal Fraction
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 the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A decimal numeral (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
