Pronunciation: /kɒnˈvɛks/ Explain

A shape is convex if a line segment that is drawn between any two points in the shape is completely contained within the shape.[1]

convex shape
Figure 1: A disc is convex

Figure 1 is an example of a convex shape, in this case a disc. Since it is not possible to pick two points within the shape and draw a line between them that leaves the shape, the shape is convex.

concave shape
Figure 2: Concave shape

Figure 2 is an example of a concave shape. Note that the entire line is not contained within the disc.

Discovery - Is a spherical solid convex or concave?

A spherical solid is a three dimensional shape with a sphere as the outer edge. Is a spherical solid concave or convex? Imagine a sphere. Can you imagine a straight line between any two points in the spherical solid that is partly outside the solid?

Click here to see the answer.

Mnemonic What is a mnemonic?


A bear wanted a nice cozy cave in which to spend the winter. She found a rock sticking out of the ground, but it vexed her that the rock was convex. She continued to look. Then she found a cave. It was concave, so she crawled in and went to sleep for the winter.


  1. Convex. Geometry Glossary. American Mathematical Society. Last Accessed 8/6/2018.
  2. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry. pg 54. Ginn & Company. 1899. Last Accessed 8/6/2018. Buy the book
  3. Lyman, Elmer A.. Plane and Solid Geometry. pg 57. American Book Company. 1908. Last Accessed 8/6/2018. Buy the book

Cite this article as:

McAdams, David E. Convex. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/18/2010: Added "References". (McAdams, David E.)
7/10/2008: Added click here to see answer. (McAdams, David E.)
7/1/2008: Initial version. (McAdams, David E.)

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