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Sicherman Dice
Comparison of sum tables of and dice. If zero is allowed, normal dice have one variant and Sicherman dice have two Each table has Sicherman dice are a pair of 6-sided dice with non-standard numbers–one with the sides 1, 2, 2, 3, 3, 4 and the other with the sides 1, 3, 4, 5, 6, 8. They are notable as the only pair of 6-sided dice that are not normal dice, bear only positive integers, and have the same probability distribution for the sum as normal dice. They were invented in 1978 by George Sicherman of Buffalo, New York. Mathematics A standard exercise in elementary combinatorics is to calculate the number of ways of rolling any given value with a pair of fair six-sided dice (by taking the sum of the two rolls). The table shows the number of such ways of rolling a given value n: Crazy dice is a mathematical exercise in elementary combinatorics, involving a re-labeling of the faces of a pair of six-sided dice to reproduce the same frequency of sums as the standard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sicherman Dice Table
Sicherman is a surname. Notable people with the surname include: * George Sicherman, inventor of the Sicherman dice * Harvey Sicherman (1945–2010), American writer and foreign policy expert See also * Scherman {{Short pages monitor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also a leading authority on Lewis Carroll. ''The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-cube Calendar
A two-cube calendar is a desk calendar consisting of two cubes with faces marked by digits 0 through 9. Each face of each cube is marked with a single digit, and it is possible to arrange the cubes so that any chosen day of the month (from 01, 02, ... through 31) is visible on the two front faces. A puzzle about the two-cube calendar was described in Gardner's column in ''Scientific American''.Gardner, Mathematical Circus, 1992, p. 186. In the puzzle discussed in ''Mathematical Circus'' (1992), two visible faces of one cube have digits 1 and 2 on them, and three visible faces of another cube have digits 3, 4, 5 on them. The cubes are arranged so that their front faces indicate the 25th day of the current month. The problem is to determine digits hidden on the seven invisible faces. Gardner wrote he saw a two-cube desk calendar in a store window in New York. According to a letter received by Gardner from John S. Singleton (England), Singleton patented the calendar in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The very first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.87. Notable publications * The 1972 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorization
In mathematics, factorization (or factorisation, see American and British English spelling differences#-ise, -ize (-isation, -ization), English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind. For example, is a factorization of the integer , and is a factorization of the polynomial . Factorization is not usually considered meaningful within number systems possessing division ring, division, such as the real number, real or complex numbers, since any x can be trivially written as (xy)\times(1/y) whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by Greek mathematics, ancient Greek mathematicians in the case of integers. They proved the fundamental theorem o ... [...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 is divisible by a nonzero integer if there exists an integer such that n=km. This is written as :m\mid n. Other ways of saying the same thing are that divides , is a divisor of , is a factor of , and is a multiple of . If does not divide , then the notation is m\not\mid n. Usually, is required to be nonzero, but is allowed to be zero. With this convention, m \mid 0 for every nonzero integer . Some definitions omit the requirement that m be nonzero. General Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Of Unity
In mathematics, a root of unity, occasionally called a Abraham de Moivre, de Moivre number, is any complex number that yields 1 when exponentiation, raised to some positive integer power . Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform. Roots of unity can be defined in any field (mathematics), field. If the characteristic of a field, characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, converse (logic), conversely, every nonzero element of a finite field is a root of unity. Any algebraically closed field contains exactly th roots of unity, except when is a multiple of the (positive) characteristic of the field. General definition An ''th root of unity'', where is a positive integer, is a number satisfying the equation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generating Function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, the ''formal'' power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers. There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence in principle has a generating function of each type (except ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Definition Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic. Many definitions of "polyhedron" have been given within particular contexts,. some more rigorous than others, and there is not universal agreement over which of these to choose. Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include shapes that are often not considered as valid polyhedr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it is the oldest continuously published magazine in the United States. ''Scientific American'' is owned by Springer Nature, which in turn is a subsidiary of Holtzbrinck Publishing Group. History ''Scientific American'' was founded by inventor and publisher Rufus Porter (painter), Rufus Porter in 1845 as a four-page weekly newspaper. The first issue of the large format newspaper was released August 28, 1845. Throughout its early years, much emphasis was placed on reports of what was going on at the United States Patent and Trademark Office, U.S. Patent Office. It also reported on a broad range of inventions including perpetual motion machines, an 1860 device for buoying vessels by Abraham Lincoln, and the universal joint which now can be found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buffalo, New York
Buffalo is the second-largest city in the U.S. state of New York (behind only New York City) and the seat of Erie County. It is at the eastern end of Lake Erie, at the head of the Niagara River, and is across the Canadian border from Southern Ontario. With a population of 278,349 according to the 2020 census, Buffalo is the 78th-largest city in the United States. The city and nearby Niagara Falls together make up the two-county Buffalo–Niagara Falls Metropolitan Statistical Area (MSA), which had an estimated population of 1.1 million in 2020, making it the 49th largest MSA in the United States. Buffalo is in Western New York, which is the largest population and economic center between Boston and Cleveland. Before the 17th century, the region was inhabited by nomadic Paleo-Indians who were succeeded by the Neutral, Erie, and Iroquois nations. In the early 17th century, the French began to explore the region. In the 18th century, Iroquois land surrounding Buffalo Creek ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dice
Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots ( pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are designed to favor some results over others for cheating or entertainment. History Dice have been used since before recorded history, and it is uncertain where they originated. It is theorized that dice developed from the practice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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