Beverton–Holt model: Difference between revisions
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{{Portal:Mathematics/Feature article|img=Riemann Sphere.jpg|img-cap=The region between two [[Loxodrome | loxodromes]] on a geometric sphere.|img-cred=Karthik Narayanaswami|more=Riemann sphere|desc=The '''Riemann sphere''' is a way of extending the [[plane (mathematics)|plane]] of [[complex number]]s with one additional [[point at infinity]], in a way that makes expressions such as | |||
:<math>\frac{1}{0} = \infty</math> | |||
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 '''CP'''<sup>1</sup>. | |||
On a purely [[algebra]]ic 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 (algebra)|field]]. However, the Riemann sphere is geometrically and analytically well-behaved, even near infinity; it is a one-[[dimension]]al [[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]].|class={{{class}}}}} | |||
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Revision as of 14:43, 20 April 2013
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