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


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  sin{hx} produces the graph on the left, and by rotating it about the y-axis we get a 'hyperboloids of one sheet. Sinhx.pngHyperboloidOfOneSheet.png

Hyperboloids can be hyperboloids of one sheet or hyperboloids of two sheets.


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


- {x^2 \over a^2} - {y^2 \over a^2} + {z^2 \over c^2}=1 \,  hyperboloid of two sheets.

These curves are graphed using the following parametric equations:




==Analyzing a Hyperboloid from 2 Dimensionals==

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