Symmetry is described as fitting under the categories of art, science, and
psychology. However, even though these topics are generally known to be openended,
symmetry is based upon a set of rules which are not elastic. This is where Livio
introduces group theory which is the language of symmetry. While a set is a random
collection, a group is defined by its rules. The properties that define them are closure,
associativity, identity, and inverse. These rules are explained with the use of an example
of the human body which possesses identity with reflections along the vertical plane. He
explains that because the body possesses these components, the symmetry
transformations make up a group. What was most interesting however, was the fact that
scientists weren’t looking for theories regarding symmetry. It showed that the beauty of
symmetry is simple and can be found without effort.
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View Full DocumentFor my project, I decided to experiment with symmetries in terms of rotational
symmetry. I made a design that would show whether shapes were still symmetrical when
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 Winter '07
 vanderveen
 180 degrees, 360 degrees, 120 degrees, 240 degrees

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