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Encyclopedia > Hyperboloid
Hyperboloid of one sheet
Hyperboloid of one sheet
Hyperboloid of two sheets
Hyperboloid of two sheets

In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation Hyperboloid of one sheet. ... Hyperboloid of one sheet. ... Hyperboloid of two sheets. ... Hyperboloid of two sheets. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... 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). ... :For other senses of this word, see dimension (disambiguation). ...

{x^2 over a^2} + {y^2 over b^2} - {z^2 over c^2}=1  (hyperboloid of one sheet),

or

- {x^2 over a^2} - {y^2 over b^2} + {z^2 over c^2}=1  (hyperboloid of two sheets)

If, and only if, a = b, it is a hyperboloid of revolution. A hyperboloid of one sheet can be obtained by revolving a hyperbola around its transversal axis. Alternatively, a hyperboloid of two sheets of axis AB is obtained as the set of points P such that AP−BP is a constant, AP being the distance between A and P. Points A and B are then called the foci of the hyperboloid. A hyperboloid of two sheets can be obtained by revolving a hyperbola around its focal axis. In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ... A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. ... In geometry, the focus (pl. ... The parabola y=x2 rotated about the z-axis A surface of revolution is a surface created by rotating a curve lying on some plane (the generatrix) around a straight line (the axis of rotation) that lies on the same plane. ... A graph of a hyperbola. ...


A hyperboloid of one sheet is a doubly ruled surface; if it is a hyperboloid of revolution, it can also be obtained by revolving a line about a skew line. In geometry, a surface is ruled if through every point of there is a straight line that lies on . ... In geometry, two lines are said to be skew lines if they do not intersect but are not parallel. ...

An elliptic hyperboloid of one sheet. The wires are straight lines. For any point on the surface, there are two straight lines lying entirely on the surface which pass through the point. This illustrates the doubly ruled nature of this surface.
An elliptic hyperboloid of one sheet. The wires are straight lines. For any point on the surface, there are two straight lines lying entirely on the surface which pass through the point. This illustrates the doubly ruled nature of this surface.

A degenerate hyperboloid is of the form Image File history File links Ruled_hyperboloid. ... Image File history File links Ruled_hyperboloid. ...

{x^2 over a^2} + {y^2 over b^2} - {z^2 over c^2}=0;

if a = b then this will give a cone, if not then it gives an elliptical cone. This article needs to be cleaned up to conform to a higher standard of quality. ...


A notable (and recognizable) use of a hyperboloid structure is in the cooling towers utilized by power stations. Cooling towers are structures for cooling water or other working medium to near-ambient temperature. ... A power station (also power plant) is a facility for the generation of electric power. ...


See also


  Results from FactBites:
 
hyperboloid (321 words)
A quadratic surface of which there are two basic forms: a hyperboloid of one sheet, generated by spinning a hyperbola around its conjugate axis, and a hyperboloid of two sheets produced by rotating a hyperbola about its transverse axis.
This fact enables a close approximation to a hyperboloid to be made in the form of a string model.
Hyperboloids are seen in the manmade world in the form of cooling towers at power stations and, most strikingly, in the shape of the McDonnell Planetarium in St. Louis, Missouri (shown above).
Connector Specifier - Medical connectors require reliability and long life (1508 words)
The hyperboloid design is constructed from a series of beryllium copper wires that stretch to accommodate the pin upon insertion.
Hyperboloid contacts are capable of withstanding extreme levels of shock and vibration while guaranteeing signal integrity, one of the main reasons that they are popular in industrial and aerospace applications.
Due to the hyperboloid socket design, specifically the 360º wrap provided by the spring wires, immunity to high levels of shock and vibration is guaranteed even when measured over periods as small as 5 ns.
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