Hyperboloid

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Hyperboloid
Hyperboloid.jpg
Field: Calculus
Image Created By: Paul Nylander
Website: Paul Nylander's Site

Hyperboloid

A hyperboloid is a quadric, a type of surface in three dimensions.


Basic Description

A hyperboloid is a 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. HyperboloidOfOneSheet.png HyperboloidOfTwoSheets.png

A More Mathematical Explanation

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

or

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{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.

Parametrizing Hyperboloids

Analyzing a Hyperboloid from 2 Dimensionals




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