what symmetry means
(3) Symmetry, in the general sense, means the invariance of the structure of a mathematical or physical object with respect to transformations of the object. For example, the symmetry of the laws of the theory of relativity is determined by their invariance with respect to the Lorentz transformations.1) A symmetry, in the narrow sense, is a reflection with respect to a plane Î± in space or with respect to a line a in the plane. Such a symmetry is a transformation of space or the plane that takes every point M into a point Mâ such that the line segment MMâ is perpendicular to Î± or a and is divided in half by Î± or a.