Editing Reflection symmetry (section)

==Symmetric function== 
[[File:Empirical Rule.PNG|thumb|A [[normal distribution]] bell curve is an example of a symmetric function|left]]

In formal terms, a [[mathematical object]] is symmetric with respect to a given [[mathematical operation|operation]] such as reflection, [[Rotational symmetry|rotation]], or [[Translational symmetry|translation]], if, when applied to the object, this operation preserves some property of the object.<ref name=Stewart32>{{cite book | title=What Shape is a Snowflake? Magical Numbers in Nature | publisher=Weidenfeld & Nicolson | author=Stewart, Ian | year=2001 | page=32}}</ref> The set of operations that preserve a given property of the object form a [[group (algebra)|group]]. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations (and vice versa).

The symmetric function of a two-dimensional figure is a line such that, for each [[perpendicular]] constructed, if the perpendicular intersects the figure at a distance 'd' from the axis along the perpendicular, then there exists another intersection of the shape and the perpendicular at the same distance 'd' from the axis, in the opposite direction along the perpendicular.

Another way to think about the symmetric function is that if the shape were to be folded in half over the axis, the two halves would be identical: the two halves are each other's [[mirror image]]s.<ref name=Stewart32/> Thus, a square has four axes of symmetry because there are four different ways to fold it and have the edges all match. A circle has infinitely many axes of symmetry, while a [[cone]] and [[sphere]] have infinitely many planes of symmetry.