Radial Symmetry

Pronunciation: /ˈreɪ di əl ˈsɪm ɪ tri/ ?

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Manipulative 1: Radial symmetry of a five pointed star. Click on the blue point in the manipulative and drag it to change the figure.

A geometric object has radial symmetry if it has congruent parts radiating out from a central point. The five-pointed star in figure 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 preimage, 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

IllustrationDescription
An apple cut in half across the middle showing five point symmetry.This apple was cut in two across the middle. Notice the five seeds radiating out from the middle.
An orange, 11 armed sea star against a dark green background.Most sea stars have 5 point symmetry. This one has 11 point symmetry.
A drawing of several sea anemones showing radial symmetry.Sea anemones have radial symmetry.
Chicory flower. A medium blue flower with many small rectangular petals radiating out from the center.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.

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Radial Symmetry. 2010-11-29. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/radialsymmetry.html.

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2010-11-29: Initial version (McAdams, David.)

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