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Mathematics from the Greek: μαθηματικά or mathēmatiká, is the study of patterns. Such patterns include quantities (numbers) and their operations, interrelations, combinations and abstractions; and of space configurations and their structure, measurement, transformations, and generalizations. Mathematics evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of positions, shapes and motions of abstract objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.
Selected article | Picture of the month | Did you know... | Topics in mathematics There are approximately 23529 mathematics articles in Wikipedia.
The Riemann sphere is a way of extending the plane of complex numbers with one additional point at infinity, in a way that makes expressions such as well-behaved and useful, at least in certain contexts. It is named after 19th century mathematician Bernhard Riemann. It is also called the complex projective line, denoted CP1. On a purely algebraic level, the complex numbers with an extra infinity element constitute a number system known as the extended complex numbers. Arithmetic with infinity does not obey all of the usual rules of algebra, and so the extended complex numbers do not form a field. However, the Riemann sphere metrically and analytically well-behaved, even near infinity; it is a one-dimensional complex manifold, also called a Riemann surface. In complex analysis, the Riemann sphere facilitates an elegant theory of meromorphic functions. The Riemann sphere is ubiquitous in projective geometry and algebraic geometry as a fundamental example of a complex manifold, projective space, and algebraic variety. It also finds utility in other disciplines that depend on analysis and geometry, such as quantum mechanics and other branches of physics.
Missing square puzzle animation. The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures. It depicts two arrangements of shapes, each of which apparently forms a 13×5 right-angled triangle, but one of which has a 1×1 hole in it. The puzzle works as the blue and red triangles are not similar so their hypotenuses are not parallel. In one arrangement the line bends one way, in one arrangement it bends the other way, and the gap between these bent lines is exactly one unit.
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