Difference between revisions of "Hyperboloid"
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|ImageIntro=A hyperboloid is a quadric, a type of surface in three dimensions. | |ImageIntro=A hyperboloid is a quadric, a type of surface in three dimensions. | ||
|ImageDescElem= | |ImageDescElem= | ||
− | A hyperboloid is a surface in 3 dimensions that is generated by rotating a hyperbolic function around an axis. | + | A hyperboloid is a quadric surface in 3 dimensions that is generated by [[revolution of line|rotating]] a hyperbolic function around an axis. |
Hyperboloids can be '''hyperboloids of one sheet''' or '''hyperboloids of two sheets'''. | Hyperboloids can be '''hyperboloids of one sheet''' or '''hyperboloids of two sheets'''. | ||
[[Image:HyperboloidOfOneSheet.png|300px]] [[Image:HyperboloidOfTwoSheets.png|300px]] | [[Image:HyperboloidOfOneSheet.png|300px]] [[Image:HyperboloidOfTwoSheets.png|300px]] | ||
+ | <math>{x^2 \over a^2} + {y^2 \over a^2} - {z^2 \over c^2}=1 \,</math> '''hyperboloid of one sheet,''' | ||
− | + | or | |
− | + | <math>- {x^2 \over a^2} - {y^2 \over a^2} + {z^2 \over c^2}=1 \,</math> '''hyperboloid of two sheets.''' | |
+ | |||
+ | These curves are graphed using the following <balloon title="Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters" style="color:green"> parametric equations: </balloon> | ||
− | <math> | + | <math>x(u,v)=a(\sqrt{1+u^2})cos{v}\,</math> |
− | = | + | <math>y(u,v)=a(\sqrt{1+u^2})sin{v}\,</math> |
+ | <math>z(u,v)=cu\,</math> | ||
==Analyzing a Hyperboloid from 2 Dimensionals== | ==Analyzing a Hyperboloid from 2 Dimensionals== | ||
+ | |||
+ | |||
+ | |||
|Pre-K=No | |Pre-K=No | ||
|Elementary=No | |Elementary=No |
Revision as of 12:27, 26 May 2009
Hyperboloid |
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Hyperboloid
- A hyperboloid is a quadric, a type of surface in three dimensions.
Basic Description
A hyperboloid is a quadric surface in 3 dimensions that is generated by rotating a hyperbolic function around an axis.
Hyperboloids can be hyperboloids of one sheet or hyperboloids of two sheets.
hyperboloid of one sheet,
or
hyperboloid of two sheets.
These curves are graphed using the following parametric equations:
==Analyzing a Hyperboloid from 2 Dimensionals==
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