Catenary

Pronunciation: /ˈkæt nˌɛr i/ ?

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

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

Figure 1: Long heavy chain forming a catenary.

Figure 1: Long thin 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.org. http://www.allmathwords.org/en/c/catenary.html.

Translations

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Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem.org and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
• Figure 1: Long heavy chain forming a catenary.: Abby Brown, Torrey Pines High School. Used by permission. http://teachers.sduhsd.k12.ca.us/abrown/Activities/Matching/answers/catenary.htm
• Figure 2: Long thin chain forming a catenary.: Abby Brown, Torrey Pines High School. Used by permission. http://teachers.sduhsd.k12.ca.us/abrown/Activities/Matching/answers/catenary.htm
• Figure 3: Thick wide chain forming a catenary.: Abby Brown, Torrey Pines High School. Used by permission. http://teachers.sduhsd.k12.ca.us/abrown/Activities/Matching/answers/catenary.htm

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.)