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Sprouts (game)
Sprouts is a paper-and-pencil game which can be analyzed for its mathematical properties. It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in the early 1960s. The setup is even simpler than the popular Dots and Boxes game, but game-play develops much more artistically and organically. Rules The game is played by two players, starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line between two spots (or from a spot to itself) and adding a new spot somewhere along the line. The players are constrained by the following rules. * The line may be straight or curved, but must not touch or cross itself or any other line. * The new spot cannot be placed on top of one of the endpoints of the new line. Thus the new spot splits the line into two shorter lines. * No spot may have more than three lines attached to it. For the purposes of this rule, a line from the spot to itself cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paper-and-pencil Game
Paper-and-pencil games or paper-and-pen games (or some variation on those terms) are games that can be played solely with paper and pencils (or other writing implements), usually without erasing. They may be played to pass the time, as icebreakers, or to end boredom. In recent times, they have been supplanted by mobile games. Some popular examples of pencil-and-paper games include Tic-tac-toe, Sprouts, Dots and Boxes, Hangman, MASH, Paper soccer, and Spellbinder. The term is unrelated to the use in role-playing games to differentiate tabletop games from role-playing video games. Board games where pieces are never moved or removed from the board once being played, particularly abstract strategy game Abstract strategy games admit a number of definitions which distinguish these from strategy games in general, mostly involving no or minimal narrative theme, outcomes determined only by player choice (with no randomness), and perfect informatio ...s like Gomoku and Conn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carnegie Mellon University
Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology in 1912 and began granting four-year degrees in the same year. In 1967, the Carnegie Institute of Technology merged with the Mellon Institute of Industrial Research, founded in 1913 by Andrew Mellon and Richard B. Mellon and formerly a part of the University of Pittsburgh. Carnegie Mellon University has operated as a single institution since the merger. The university consists of seven colleges and independent schools: The College of Engineering, College of Fine Arts, Dietrich College of Humanities and Social Sciences, Mellon College of Science, Tepper School of Business, Heinz College of Information Systems and Public Policy, and the School of Computer Science. The university has its main campus located 5 miles (8 km) from Dow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Games
A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. Often, such games have simple rules and match procedures, such as Tic-tac-toe and Dots and Boxes. Generally, mathematical games need not be conceptually intricate to involve deeper computational underpinnings. For example, even though the rules of Mancala are relatively basic, the game can be rigorously analyzed through the lens of combinatorial game theory. Mathematical games differ sharply from mathematical puzzles in that mathematical puzzles require specific mathematical expertise to complete, whereas mathematical games do not require a deep knowledge of mathematics to play. Often, the arithmetic core of mathematical games is not readily apparent to players untrained to note the statistical or mathematical aspects. Some mathematical games are of deep interest in the field of recreational mathematics. When studying a game's core mathematics, arithmetic theory i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Utah
The University of Utah (U of U, UofU, or simply The U) is a public research university in Salt Lake City, Utah. It is the flagship institution of the Utah System of Higher Education. The university was established in 1850 as the University of Deseret () by the General Assembly of the provisional State of Deseret, making it Utah's oldest institution of higher education. It received its current name in 1892, four years before Utah attained statehood, and moved to its current location in 1900. As of Fall 2019, there were 24,485 undergraduate students and 8,333 graduate students, for an enrollment total of 32,818, making it the second largest public university in the state after Utah Valley University. Graduate studies include the S.J. Quinney College of Law and the School of Medicine, Utah's first medical school. It is a member of the Association of American Universities (AAU) and is classified among "R1: Doctoral Universities – Very high research activity". According to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penguin Books
Penguin Books is a British 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."About Penguin – company history" , Penguin Books. Penguin revolutionised publishing in the 1930s through its inexpensive s, sold through and other stores for sixpence, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard K
Richard is a male given name. It originates, via Old French, from Old Frankish and is a compound of the words descending from Proto-Germanic ''*rīk-'' 'ruler, leader, king' and ''*hardu-'' 'strong, brave, hardy', and it therefore means 'strong in rule'. Nicknames include "Richie", "Dick", "Dickon", " Dickie", " Rich", "Rick", " Rico", " Ricky", and more. Richard is a common English, German and French male name. It's also used in many more languages, particularly Germanic, such as Norwegian, Danish, Swedish, Icelandic, and Dutch, as well as other languages including Irish, Scottish, Welsh and Finnish. Richard is cognate with variants of the name in other European languages, such as the Swedish "Rickard", the Catalan "Ricard" and the Italian "Riccardo", among others (see comprehensive variant list below). People named Richard Multiple people with the same name * Richard Andersen (other) * Richard Anderson (other) * Richard Cartwright (other) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elwyn R
Elwyn is an unincorporated community located in Middletown Township, Delaware County, Pennsylvania Middletown Township is a township in Delaware County, Pennsylvania, United States. The population was 15,807 at the 2010 census. The Pennsylvania State University has an undergraduate satellite campus called Penn State Brandywine located in the ..., USA. Elwyn has a latitude of 39.907N, longitude of -75.41W and an elevation of 253 feet above sea level. Elwyn is home to Elwyn Inc., a facility caring for the needs of the developmentally disabled and disadvantaged. Elwyn is named for Dr. Alfred L. Elwyn, a physician who founded ''The Pennsylvania Training School for Feeble-minded Children'' in 1852 with teacher James B. Richards. See also * Media Area References External linksElwyn Inc. facility official site {{authority control Unincorporated communities in Delaware County, Pennsylvania Unincorporated communities in Pennsylvania ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent. It is commonly denoted by \chi ( Greek lower-case letter chi). The Euler characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification of the Platonic solids. It was stated for Platonic solids in 1537 in an unpublished manuscript by Francesco Maurolico. Leonhard Euler, for whom the concept is named, introduced it for convex polyhedra more generally but failed to rigorously prove that it is an invariant. In modern mathematics, the Euler characteristic arises from homology and, more abstractly, homological algebra. Polyhedra The Euler characteristic \chi was classically defined for the surfaces of polyhedra, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brussels Sprout
The Brussels sprout is a member of the Gemmifera cultivar group of cabbages (''Brassica oleracea''), grown for its edible buds. The leaf vegetables are typically 1.5–4.0 cm (0.6–1.6 in) in diameter and resemble miniature cabbages. The Brussels sprout has long been popular in Brussels, Belgium, from which it gained its name. Etymology Although native to the Mediterranean region with other cabbage species, Brussels sprouts first appeared in northern Europe during the 5th century, later being cultivated in the 13th century near Brussels, Belgium, from which they derived their name. Its group name Gemmifera (or lowercase and italicized ''gemmifera'' as a variety name) means ' (bud-producing). Cultivation Forerunners to modern Brussels sprouts were probably cultivated in Ancient Rome. Brussels sprouts as they are now known were grown possibly as early as the 13th century in what is now Belgium. The first written reference dates to 1587. During the 16th century, they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brussel Sprouts Game
Brussels (french: Bruxelles or ; nl, Brussel ), officially the Brussels-Capital Region (All text and all but one graphic show the English name as Brussels-Capital Region.) (french: link=no, Région de Bruxelles-Capitale; nl, link=no, Brussels Hoofdstedelijk Gewest), is a region of Belgium comprising 19 municipalities, including the City of Brussels, which is the capital of Belgium. The Brussels-Capital Region is located in the central portion of the country and is a part of both the French Community of Belgium and the Flemish Community, but is separate from the Flemish Region (within which it forms an enclave) and the Walloon Region. Brussels is the most densely populated region in Belgium, and although it has the highest GDP per capita, it has the lowest available income per household. The Brussels Region covers , a relatively small area compared to the two other regions, and has a population of over 1.2 million. The five times larger metropolitan area of Brusse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulo Operation
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is the remainder of the Euclidean division of by , where is the dividend and is the divisor. For example, the expression "5 mod 2" would evaluate to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3. Although typically performed with and both being integers, many computing systems now allow other types of numeric operands. The range of values for an integer modulo operation of is 0 to inclusive ( mod 1 is always 0; is undefined, possibly resulting in a division by zero error in some programming languages). See Modular arithmetic for an older and related c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nimber
In mathematics, the nimbers, also called ''Grundy numbers'', are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim. The nimbers are the ordinal numbers endowed with ''nimber addition'' and ''nimber multiplication'', which are distinct from ordinal addition and ordinal multiplication. Because of the Sprague–Grundy theorem which states that every impartial game is equivalent to a Nim heap of a certain size, nimbers arise in a much larger class of impartial games. They may also occur in partisan games like Domineering. Nimbers have the characteristic that their Left and Right options are identical, following a certain schema, and that they are their own negatives, such that a positive ordinal may be added to another positive ordinal using nimber addition to find an ordinal of a lower value. The minimum excludant operation is applied to sets of nimbers. Uses Nim Nim is a game in which two players take turns removing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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