Symmetry doesn't have a "history" - it has always been
present as a natural phenomenon. Symmetry is found as a basic property of some natural
objects (certain kinds of crystals, for instance - think of snowflakes), various types
of interactions (think of musical harmonies) and in many relationships. Symmetry has
been used in architecture for thousands of years by cultures around the
world.
In adding "math" as a tag to your question, I'm
guessing you are working with symmetry in mathematical processes - perhaps looking at
graphing symmetrical lines to answer equations. The process of identifying and
recognizing such situations varies with each type of problem, so you could trace the
history of the person who developed the particular type of math you are
considering.
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