What is symmetric?

Symmetry can refer to a property of both geometric objects and mathematical functions.

In geometry, symmetry is a term used to describe the property of an object that looks the same when one part of it is reflected or rotated to match another part. A symmetrical shape or object is one that has corresponding parts which match each other in size, shape and position. For example, a square is symmetrical because it has four equal sides and all its angles are right angles.

Symmetric functions are those which satisfy the condition that replacing the variable with its negative produces the same output. For example, the function f(x) = x^2 is symmetric because f(-x) = f(x^2) = (-x)^2 = x^2. Symmetric functions have useful properties in mathematics and physics, often making them easier to work with than non-symmetric functions.

Symmetry is a fundamental idea in mathematics and is found in many areas of science and nature, from snowflakes and sea shells to the laws of physics. It is an essential concept in fields such as geometry, algebra, trigonometry, calculus, and group theory.