# 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:

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 2: Long thin chain forming a catenary.
 Figure 3: Thick wide chain forming a catenary.

### References

1. McAdams, David E.. All Math Words Dictionary, catenary. 2nd Classroom edition 20150108-4799968. pg 30. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Catenary. 3/1/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/catenary.html.

### Image Credits

• 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

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)