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Symmetry in Nature

Explore connections in mathematics and nature with this article on the symmetry in nature.
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Symmetry in Nature

Symmetry surrounds you. Look down at your body. Look at the shapes on the screen. Look at the buildings on your street. Look at your cat or dog. Symmetry is variously defined as "proportion," "perfect, or harmonious proportions," and "a structure that allows an object to be divided into parts of an equal shape and size." When you think of symmetry, you probably think of some combination of all these definitions. That's because symmetry, whether in biology, architecture, art, or geometry reflects all of those definitions.

The two main types of symmetry are reflective and rotational. Reflective, or line, symmetry means that one half of an image is the mirror image of the other half (think of a butterfly's wings). Rotational symmetry means that the object or image can be turned around a center point and match itself some number of times (as in a five-pointed star).

In biology, there are three classifications of symmetry found in living organisms. Point symmetry (a kind of reflective symmetry) means that any straight cut through the center point divides the organism into mirroring halves. Some floating animals with radiating parts, and some microscopic protozoa fit into this category. Animals with this layout are all very small. Radial symmetry (a kind of rotational symmetry) means that a cone or disk shape is symmetrical around a central axis. Starfish, sea anemones, jellyfish, and some flowers have radial symmetry. Lastly, plane or bilateral symmetry (also reflective symmetry) means that a body can be divided by a central (sagittal) plane into two equal halves that form mirror images of each other. Human beings, insects, and mammals all show bilateral symmetry.

Man is naturally attracted to symmetry. Very often we consider a face beautiful when the features are symmetrically arranged. We are drawn to even proportions. In this, we are not alone. Many animals choose mates on the basis of symmetry, or a lack of asymmetrical features. Biologists believe the absence of asymmetry is an indicator of fitness (good genes), since only a healthy organism can maintain a symmetrical plan throughout its development in the face of environmental stresses, such as illness or lack of food. A symmetrical animal is usually a healthy animal. The same goes for humans.

Symmetrical forms can be found in the inanimate world as well. The planets, with slight variation due to chance, exhibit radial symmetry. Snowflakes also provide an example of radial symmetry. All snowflakes show a hexagonal symmetry around an axis that runs perpendicular to their face. Every one sixth of a revolution around this axis produces a design identical to the original. The fact that all snowflakes have this sort of symmetry is due to the way water molecules arrange themselves when ice forms. It's a reminder that symmetry is part of the structure of the world around us.

Things to Think About...
1. What advantage does a bilaterally symmetrical structure have for humans? For horses?
2. Most animals are not symmetrical with respect to a cross-sectional plane (i.e., one that parallels your waist). Why?
3. Why are planets spherical? What would happen if they were lopsided? Try spinning a top with an object stuck to its side. What happens?
4. If a stone falls into a pond, in which direction do the resulting waves travel? Why?

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