Catenary

Pronunciation: /ˈkæt nˌɛr i/ ?

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Manipulative 1: Catenary. Created with GeoGebra.

A catenary is the shape a wire makes when hanging from two telephone poles.[1] While it looks like a parabola, it is a hyperbolic cosine function. The general formula for a catenary is:

f(x)=a*cosh((x-h)/2)+k

where h is the horizontal offset and k is the vertical offset.

The following images are various chains suspended from their ends, forming catenaries.

Long heavy chain forming a catenary.
Figure 1: Long heavy chain forming a catenary.
Long thin chain forming a catenary.
Figure 1: Long thin chain forming a catenary.
Thick wide chain forming a catenary.
Figure 1: Thick wide chain forming a catenary.

Cite this article as:


Catenary. 2010-01-09. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/catenary.html.

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Revision History


2010-01-09: Added "References" (McAdams, David.)
2009-09-08: Added images of catenaries and corrected a grammar error. (McAdams, David.)
2008-11-25: Changed equations to images (McAdams, David.)
2008-11-20: Initial version (McAdams, David.)

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