Catenary

Pronunciation: /ˈkæt nˌɛr i/ Explain

Click on the blue points and drag them to change the figure.

Can you make the shape open downwards?
Manipulative 1 - Catenary Created with GeoGebra.

A catenary is the shape a wire makes when hanging from two telephone poles. While it may look like a parabola, actually 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 2: Long thin chain forming a catenary.
Thick wide chain forming a catenary.
Figure 3: Thick wide chain forming a catenary.

Cite this article as:

McAdams, David E. Catenary. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/catenary.html.

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 LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
  • Long heavy chain forming a catenary: Abby Brown, http://teachers.sduhsd.k12.ca.us. Used by permission.
  • Long thin chain forming a catenary: Abby Brown, http://teachers.sduhsd.k12.ca.us. Used by permission.
  • Thick wide chain forming a catenary: Abby Brown, http://teachers.sduhsd.k12.ca.us. Used by permission.

Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/9/2010: Added "References". (McAdams, David E.)
9/8/2009: Added images of catenaries and corrected a grammar error. (McAdams, David E.)
11/25/2008: Changed equations to images. (McAdams, David E.)
11/20/2008: Initial version. (McAdams, David E.)

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License