Radial Symmetry

Pronunciation: /ˈreɪ.di.əl ˈsɪm.ɪ.tri/ Explain

Click on the blue point and drag it to change the figure. In a full circle, how many times the the red star lay exactly on top of the black star? Manipulative 1 - Radial Symmetry of a Five Pointed Star Created with GeoGebra.

A geometric object has radial symmetry if it has congruent parts radiating out from a central point. The five-pointed star in manipulative 1 has radial symmetry. Each of the points is identical to the other points. All of the points extend out the same way from the central point. Another way to think of radial symmetry, involves rotating the object around the central point. If the object is rotated by any angle other than a full circle and lies exactly on top of the pre-image, then the object has radial symmetry. Objects that are radially symmetric can differ on how many points of symmetry they have. The star in figure 1 has 5 point radial symmetry. In nature, there are many plants and animals that have 3 point, 5 point, 6 point and 8 point symmetry. Some of these are shown in the table below.

Radial Symmetry in Nature

Illustration	Description
	This apple was cut in two across the middle. Notice the five seeds radiating out from the middle.
	Most sea stars have 5 point symmetry. This one has 11 point symmetry.
	Sea anemones have radial symmetry.
	A chicory flower has radial symmetry. The different levels of petals each have radial symmetry and are offset from each other.
Table 1: Radial symmetry in nature. Click on the images to see a larger version.

References

1. McAdams, David E.. All Math Words Dictionary, radial symmetry. 2nd Classroom edition 20150108-4799968. pg 149. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Radial Symmetry. 3/28/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/r/radialsymmetry.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
• Apple showing radial symmetry: Rasbak, https://en.wikipedia.org. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Sterappel_dwarsdrsn.jpg.
• Sea Star: Hase Benutzer, https://en.wikipedia.org. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Eleven-Armed_Sea_Star.jpg.
• Sea Anemones: Ernst Haeckek, https://en.wikipedia.org. Copyright has expired. https://en.wikipedia.org/wiki/File:Haeckel_Actiniae.jpg.
• Chicory flower: Sue Sweeney, https://commons.wikimedia.org. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. https://commons.wikimedia.org/wiki/File:Chicory_flower.jpg.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
8/28/2018: Corrected spelling. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)