Why Teach Symmetry?
Symmetry is found everywhere in nature and is also one of the most prevalent themes in art, architecture, and design — in cultures all over the world and throughout human history. Symmetry is certainly one of the most powerful and pervasive concepts in mathematics. In the Elements, Euclid exploited symmetry from the very first proposition to make his proofs clear and straightforward. Recognizing the symmetry that exists among the roots of an equation, Galois was able to solve a centuries-old problem. The tool that he developed to understand symmetry, namely group theory, has been used by mathematicians ever since to define, study, and even create symmetry. Students are fascinated by concrete examples of symmetry in nature and in art. The study of symmetry can be as elementary or as advanced as one wishes; for example, one can simply locate the symmetries of designs and patterns, or one use symmetry groups as a comprehensible way to introduce students to the abstract approach of modern
