Symmetry

Symmetry is a property of some geometrical objects. Objects with symmetry appear the same when reflected along an axis or when rotated around a point. An object with symmetry is said to be symmetrical. The opposite of symmetry is asymmetry, which describes an object that does not have symmetry.

Examples of symmetry in shapes.

3-rotational symmetry

Leonardo da Vinci's Vitruvian Man (ca. 1487) is often used as a representation of symmetry in the human body and, by extension, the natural universe.

Symmetric arcades of a portico in the Great Mosque of Kairouan also called the Mosque of Uqba, in Tunisia.

In reflectional symmetry, the axis of symmetry must cross the shape through the middle, dividing it into equal halves. In rotational symmetry, the object is identical when it is rotated by a certain amount.

There are many ways to see the idea of symmetry in different things. Symmetrical objects can be material, such as a crystal, a quilt, a living being, floor tiles, or a molecule. Transformations such as moving across a regularly patterned tile floor and rotating an eight-sided vase show those objects' symmetry. A set of objects sharing a spatial relationship could be symmetrical.

Abstract structures can also have symmetry, such as a mathematical equation or in the way music is played (as in a series of tones). Symmetry may be found with respect to the passage of time; it can be seen as an aspect of scientific models, language, music and even knowledge itself.^[1]