Difference between revisions of "Hyperboloid"
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They are represented by the following equations. | They are represented by the following equations. | ||
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<math>{x^2 \over a^2} + {y^2 \over a^2} - {z^2 \over c^2}=1 \,</math> '''hyperboloid of one sheet,''' | <math>{x^2 \over a^2} + {y^2 \over a^2} - {z^2 \over c^2}=1 \,</math> '''hyperboloid of one sheet,''' | ||
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<math>- {x^2 \over a^2} - {y^2 \over a^2} + {z^2 \over c^2}=1 \,</math> '''hyperboloid of two sheets.''' | <math>- {x^2 \over a^2} - {y^2 \over a^2} + {z^2 \over c^2}=1 \,</math> '''hyperboloid of two sheets.''' | ||
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These curves can also be defined 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> | These curves can also be defined 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> | ||
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==Analyzing a Hyperboloid from 2 Dimensionals== | ==Analyzing a Hyperboloid from 2 Dimensionals== | ||
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+ | ==Other Uses== | ||
+ | The construction of a 1 sheeted hyperboloid can be approximated by having two circles connected by many straight beams. This structure is used most recognizably in nuclear cooling towers. | ||
Revision as of 13:30, 26 May 2009
Hyperboloid |
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Hyperboloid
- A hyperboloid is a quadric, a type of surface in three dimensions.
Contents
Basic Description
A hyperboloid is a quadric surface in 3 dimensions that is generated by rotating a hyperbolic function around an axis.
The hyperbolic function produces the graph on the left, and by rotating it about the y-axis we get a hyperboloids of one sheet.
The hyperbolic function produces the graph on the left, and by rotating it about the y-axis we get a hyperboloids of one sheet.
They are represented by the following equations.
hyperboloid of one sheet,
or
hyperboloid of two sheets.
These curves can also be defined using the following parametric equations:
Analyzing a Hyperboloid from 2 Dimensionals
Other Uses
The construction of a 1 sheeted hyperboloid can be approximated by having two circles connected by many straight beams. This structure is used most recognizably in nuclear cooling towers.
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