Monday, March 26, 2007

What is Symmetry?

Symmetry can be a very abstract concept for both teachers and students. To begin, there are many definitions explaining what symmetry truly is. Numerous responses to the question "What is symmetry?" can be found, however there are certain commonalities amongst them. Symmetry is a topic found within the field of geometry. Geometry deals with the spatial relations of lines, angles, surfaces and solids, while symmetry involves the parts of a figure corresponding in size, shape and position on either side of a dividing line, or round a center (Liebeck and Pollard, 1995). Simply put, a figure has symmetry when it can be divided equally in a minimum of two parts, with both parts having identical characteristics.

The website identifies three types of symmetry: reflection, rotational and point. A brief overview of each type is listed below.

Reflection Symmetry- Often called line or mirror symmetry, it is when a figure is divided into two parts and one half is the reflection of the other half. The line separating both sides of the figure is referred to as the Line of Symmetry.

Rotational Symmetry- Occurs when a figure can be rotated around a central point, at least two times, and still looks the same. The number of matches the figure makes as it is rotated once around is called the Order.

Point Symmetry- A figure that looks the same upside down or from opposite direction and has all parts matching has point, or origin symmetry. The origin is the central point around which the figure is symmetrical.

Symmetry can be found in mathematics, science, nature, art and the body, just to name a few. This blog will attempt to discuss symmetry with a focus on mathematics instruction.