4.5: Symmetry

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In 2D geometry, a figure is symmetrical if an operation can be performed on it that leaves it occupying the same physical space. This can be accomplished in two ways.

Line symmetry

Line symmetry occurs when a line can be drawn through an object such that both halves of the object are mirror images of each other.

Example $\PageIndex{1}$:

Consider the triangle below. An equilateral triangle has three lines of symmetry, one from each vertex to the midpoint of the opposite side.

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Rotational Symmetry

Rotational symmetry occurs when a shape may be rotated to occupy the same space as the original.

Example $\PageIndex{2}$:

Let's take the same triangle again. An equilateral triangle has order-three rotational symmetry: 120°, 240°, and 360 °. Once we have determined rotational symmetry to 360 degrees, we can stop, as the pattern will repeat itself after that.

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Symmetry in Art

Symmetry in art is used to emphasize beauty and order. The human brain finds symmetry to be attractive and beautiful. For this reason, artists attempt to emphasize (at certain times and using certain methods) the symmetry of their subject or surroundings.

Triskelions are an example of rotational symmetry.

$965px-Triple-Spiral-Symbol.svg.png$

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