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In mathematics, an annulus (the Latin word for "little ring", with plural annuli) is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. The adjective form is annular (for example, an annular eclipse). Image File history File links Simple drawing of an annulus. ...
Image File history File links Simple drawing of an annulus. ...
Euclid, detail from The School of Athens by Raphael. ...
It has been suggested that History of the Latin language be merged into this article or section. ...
For Solar Eclipse, the alien friend of the rubber doll Betty Spaghetty, see Betty Spaghetty Photo taken by John Walker during the Zambia 2001 eclipse A solar eclipse occurs when the Sun, Moon and Earth are on a single line with the Moon in the middle. ...
The open annulus is topologically equivalent to the open cylinder  . This word should not be confused with homomorphism. ...
A right circular cylinder In mathematics, a cylinder is a quadric, i. ...
The area of such an annulus is given by the difference in the areas of a circle of radius R and one of radius r: In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ...
 This result can be obtained via calculus by dividing the annulus up into an infinite number of annuli of infinitesimal width dρ and area 2πρdρ ( = circumference × width) and then integrating from ρ = r to ρ = R: Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ...
In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ...
In calculus, the integral of a function is a generalization of area, mass, volume and total. ...
 Interestingly, the area of an annulus can also be obtained by multiplying pi by the square of half of the length of the longest interval that can lie completely inside the annulus.
Complex structure
In complex analysis an annulus ann(a; r, R) in the complex plane is an open region defined by: Complex analysis is the branch of mathematics investigating functions of complex numbers, and is of enormous practical use in many branches of mathematics, including applied mathematics. ...
In mathematics, the complex plane is a way of visualising the space of the complex numbers. ...
In topology and related fields of mathematics, a set U is called open if, intuitively speaking, you can wiggle or change any point x in U by a small amount in any direction and still be inside U. In other words, if x is surrounded only by elements of U...
 If r is 0, the region is known as the punctured disk of radius R around the point a.
As a subset of the complex plane, an annulus can be considered as a Riemann surface. The complex structure of an annulus depends only on the ratio r/R. Each annulus ann(a; r, R) can be holomorphically mapped to a standard one centered at the origin and with outer radius 1 by the map Two intersecting planes in R3 In mathematics, a plane is a fundamental two-dimensional object. ...
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold. ...
Holomorphic functions are the central object of study of complex analysis; they are functions defined on an open subset of the complex number plane C with values in C that are complex-differentiable at every point. ...
 The inner radius is then r/R < 1.
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