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Symmetry, in general, defines an agreement in dimensions, due proportion, arrangement. Symmetry also refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, that an object is invariant to a transformation, such as reflection but including other transforms. Although these two meanings of "symmetry" can sometimes be mutually exclusive, they are related, so in this book they are discussed together. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations such as scaling, reflection, and rotation; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music. Symmetry also plays a very important role in theorizing mathematical models in Physics and Cosmology. A simple example of the importance and value in the principle of symmetry is Newtons third law of motion which specifies that "every action must have an equal and opposite reaction." This law is the essence of symmetry in its many forms.
