Portal:Mathematics
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Mathematics is the study of numbers, quantity, space, structure, and change. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.
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There are approximately 31,444 mathematics articles in Wikipedia.
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All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Image credit: User:Tttrung 
The trigonometric functions are functions of an angle; they are most important when studying triangles and modeling periodic phenomena, among many other applications. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to complex numbers.
The study of trigonometric functions dates back to Babylonian times, and a considerable amount of fundamental work was done by ancient Greek, Indian and Arab mathematicians.
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Conway's Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is an example of a zeroplayer game, meaning that its evolution is completely determined by its initial state, requiring no further input as the game progresses. After an initial pattern of filledin squares ("live cells") is set up in a twodimensional grid, the fate of each cell (including empty, or "dead", ones) is determined at each step of the game by considering its interaction with its eight nearest neighbors (the cells that are horizontally, vertically, or diagonally adjacent to it) according to the following rules: (1) any live cell with fewer than two live neighbors dies, as if caused by underpopulation; (2) any live cell with two or three live neighbors lives on to the next generation; (3) any live cell with more than three live neighbors dies, as if by overcrowding; (4) any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction. By repeatedly applying these simple rules, extremely complex patterns can emerge. In this animation, a breeder (in this instance called a puffer train, colored red in the final frame of the animation) leaves guns (green) in its wake, which in turn "fire out" gliders (blue). Many more complex patterns are possible. Conway developed his rules as a simplified model of a hypothetical machine that could build copies of itself, a more complicated version of which was discovered by John von Neumann in the 1940s. Variations on the Game of Life use different rules for cell birth and death, use more than two states (resulting in evolving multicolored patterns), or are played on a different type of grid (e.g., a hexagonal grid or a threedimensional one). After making its first public appearance in the October 1970 issue of Scientific American, the Game of Life popularized a whole new field of mathematical research called cellular automata, which has been applied to problems in cryptography and errorcorrection coding, and has even been suggested as the basis for new discrete models of the universe.
Did you know...
 ...that the line separating the numerator and denominator of a fraction is called a solidus if written as a diagonal line or a vinculum if written as a horizontal line?
 ...that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type the complete works of William Shakespeare?
 ... that there are 115,200 solutions to the ménage problem of permuting six femalemale couples at a twelveperson table so that men and women alternate and are seated away from their partners?
 ... that mathematician Paul Erdős called the Hadwiger conjecture, a stillopen generalization of the fourcolor problem, "one of the deepest unsolved problems in graph theory"?
 ...that the six permutations of the vector (1,2,3) form a regular hexagon in 3d space, the 24 permutations of (1,2,3,4) form a truncated octahedron in four dimensions, and both are examples of permutohedra?
 ...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14piece tiling puzzle similar to tangram?
 ...that some functions can be written as an infinite sum of trigonometric polynomials and that this sum is called the Fourier series of that function?
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