Difference between revisions of "Hyperboloid"
Line 10: | Line 10: | ||
[[Image:Sinhx.png|300px]][[Image:HyperboloidOfOneSheet.png|300px]] | [[Image:Sinhx.png|300px]][[Image:HyperboloidOfOneSheet.png|300px]] | ||
− | + | [[Image:Coshx.png|300px]] [[Image:HyperboloidOfTwoSheets.png|300px]] | |
− | |||
+ | |||
+ | They are represented by the following equations. | ||
<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,''' | ||
Line 19: | Line 20: | ||
<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.''' | ||
− | These curves | + | 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> |
<math>x(u,v)=a(\sqrt{1+u^2})cos{v}\,</math> | <math>x(u,v)=a(\sqrt{1+u^2})cos{v}\,</math> |
Revision as of 13:02, 26 May 2009
Hyperboloid |
---|
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.
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==
Teaching Materials
- There are currently no teaching materials for this page. Add teaching materials.
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.