Glide reflection combines translation and reflection. In this symmetry operation, a shape is moved a constant distance and then reflected; that is, the shape is oriented in an opposite direction. Many ornamental borders utilize this combination of symmetry operations.

In dance, glide reflection patterns can often be created by having dancers face in different directions. For example, in a line extending across the stage, the dancers alternate facing downstage or upstage. Or two lines of dancers stand facing each other then and cross through each other’s lines, heading in opposite directions.… Read More

Translational symmetry involves repeating the same shape simply by shifting it a constant distance, usually in a line.  This type of symmetry can be found in many man-made objects, such as a row of evenly spaced identical pillars or the slats in a Venetian blind.

In dance, the choreography for the chorus line or the corps de ballet often utilizes translational symmetry.  The precision marching of soldiers on parade and even an unruly conga line will also display translational symmetry.

The Rockettes of Radio City Music Hall combine symmetry operations with synchronous timing to create the precise group patterns for which they are rightly famous.… Read More

A symmetry operation has to do with moving a shape through space in various ways and repeating the shape. The pattern is created through repetition. In rotational symmetry, shapes are moved in equal distances around an imaginary axis. For example, flower petals arrayed around the center of the blossom have rotational symmetry.

Circle dances performed by a group are the most obvious example of rotational symmetry. But a soloist can also create rotational symmetry simply by making a series of quarter turns and repeating an action or pose.… Read More