# Difference between revisions of "Hyperboloid"

Hyperboloid
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. Image:HyperboloidOfOneSheet.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,

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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.