Convex

Pronunciation: /kɒnˈvɛks/ ?

A shape is convex if a line 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?

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.

Picture

Painted Cave, one of the world's largest sea caves, Santa Cruz Island, California
Image 1: Painted Cave, one of the world's largest sea caves, Santa Cruz Island, California.
Think of a cave. The inside of the cave is not part of the rock, but is enclosed by rock. Notice that if you stretch a string from one side of a cave to the other, the line leaves the rock. So a cave is concave.

References

  1. convex. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=convex&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Convex. ams.org. Geometry Glossary. American Mathematical Society. (Accessed: 2010-02-05). http://www.ams.org/featurecolumn/archive/geometry-glossary.html.
  3. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry, pg 54. Ginn & Company, 1899. (Accessed: 2010-01-18). http://www.archive.org/stream/newplaneandsoli02smitgoog#page/n69/mode/1up/search/convex.
  4. Lyman, Elmer A.. Plane and Solid Geometry, pg 57. American Book Company, 1908. (Accessed: 2010-01-18). http://www.archive.org/stream/planesolidgeomet00lymarich#page/57/mode/1up/search/convex.

Cite this article as:


Convex. 2010-01-18. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/convex.html.

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Revision History


2010-01-18: Added "References" (McAdams, David.)
2008-07-10: Added click here to see answer (McAdams, David.)
2008-07-01: Initial version (McAdams, David.)

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