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Encyclopedia > Cylinder (geometry)
A right circular cylinder
A right circular cylinder
An elliptic cylinder
An elliptic cylinder

In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: Image File history File links Cylinder_geometry. ... Image File history File links Cylinder_geometry. ... Image File history File links Download high-resolution version (1200x1200, 632 KB) Here is a POV-Ray source of this image: // +FN +UA +W1200 +H1200 +A0. ... Image File history File links Download high-resolution version (1200x1200, 632 KB) Here is a POV-Ray source of this image: // +FN +UA +W1200 +H1200 +A0. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... This is an article about quadric in mathematics, to see the computing company go to Quadrics. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...

left(frac{x}{a}right)^2 + left(frac{y}{b}right)^2 = 1.

This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). Even more general is the generalized cylinder: the cross-section can be any curve. A 3-D view of a beverage-can stove with a cross section in yellow. ...

The cylinder is a degenerate quadric because at least one of the coordinates (in this case z) does not appear in the equation. By some definitions the cylinder is not considered to be a quadric at all. Ellipsoid Elliptic Paraboloid Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Cone Elliptic Cylinder Hyperbolic Cylinder Parabolic Cylinder In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). ...

In common usage, a cylinder is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by Remote Authentication Dial In User Service (RADIUS) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... For other uses, see Volume (disambiguation). ...

V = pi r^2 h ,

and its surface area is Area is the measure of how much exposed area any two dimensional object has. ...

A = 2 pi r^2 + 2 pi r h = 2 pi r ( r + h ).,

For a given volume, the cylinder with the smallest surface area has h = 2r. For a given surface area, the cylinder with the largest volume has h = 2r, i.e. the cylinder fits in a cube (height = diameter.)

There are other more unusual types of cylinders. These are the imaginary elliptic cylinders:

left(frac{x}{a}right)^2 + left(frac{y}{b}right)^2 = -1

the hyperbolic cylinder:

left(frac{x}{a}right)^2 - left(frac{y}{b}right)^2 = 1

and the parabolic cylinder:

x^2 + 2ay = 0. ,

See also

Articles like Different types of cylinder e.g. circular cylinder, intersection of cylinders especially like circular cylinder with strait cylinder to be added here! In geometry, the Steinmetz solid is the solid body generated by the intersection of two or more cylinders of equal radius at right angles. ... In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. ...

External links

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Cylinder (geometry)

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cylinder, in mathematics, surface generated by a line moving parallel to a given fixed line and continually intersecting a given fixed curve called the directrix; each line of the family of lines forming the cylinder is called a ruling, or generator.
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