Pronunciation: /ˈɛn.vəˌloʊp/ Explain

Animated image showing the creation of an envelope from a family of lines.
Figure 1: Creation of an envelope.

In mathematics, an envelope is a curve that is tangent to a family of lines or other geometric shapes. Figure 1 shows the creation of an envelope from a family of lines. Manipulative 1 shows two blue lines that are envelopes for a family of circles.

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

What would the circles look like if the two blue envelope lines were concurrent?
Manipulative 1 - Envelope of Circles Created with GeoGebra.


  1. McAdams, David E.. All Math Words Dictionary, envelope. 2nd Classroom edition 20150108-4799968. pg 70. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Envelope. 3/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/envelope.html.

Image Credits

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/24/2010: Added "References". (McAdams, David E.)
11/18/2008: Changed manipulative to GeoGebra. (McAdams, David E.)
5/10/2008: Initial version. (McAdams, David E.)

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