# Convex

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.[2]

 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.

 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?

### Mnemonic What is a mnemonic?

#### Story

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.

### References

1. McAdams, David E.. All Math Words Dictionary, convex. 2nd Classroom edition 20150108-4799968. pg 47. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Convex. Geometry Glossary. American Mathematical Society. Last Accessed 6/25/2018. http://www.ams.org/featurecolumn/archive/geometry-glossary.html.
3. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry. pg 54. www.archive.org. Ginn & Company. 1899. Last Accessed 6/25/2018. http://www.archive.org/stream/newplaneandsoli02smitgoog#page/n69/mode/1up/search/convex. Buy the book
4. Lyman, Elmer A.. Plane and Solid Geometry. pg 57. www.archive.org. American Book Company. 1908. Last Accessed 6/25/2018. http://www.archive.org/stream/planesolidgeomet00lymarich#page/57/mode/1up/search/convex. Buy the book

McAdams, David E. Convex. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/convex.html.

### Revision History

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