Rotational Symmetry

You may have often heard of the term ‘symmetry’ in the day to day life. It is a balanced and proportionate similarity found in two halves of an object, that is, one-half is the mirror image of the other half. And a shape that is not symmetrical is referred to as asymmetrical. Symmetry is found all around us, in nature, in architecture and in art. It may be explored when you flip, slide or turn an object. There may be different types of symmetry - reflection, translational and rotational symmetry.

What is Rotational Symmetry?

If a figure is rotated around a center point and it still appears exactly like it did before the rotation, it is said to have a rotational symmetry. A number of shapes like squares, circles, regular pentagons, etc. have rotational symmetry.

Center of Rotation

For a figure or object that has a rotational symmetry, the fixed point around which the rotation occurs is called the center of rotation. Example: the center of rotation of a windmill is the center of the windmill from which its blades originate.

Angle of Rotation

For a figure or object that has a rotational symmetry, the angle of turning during rotation is called the angle of rotation. Example: when a square is rotated by 90 degrees, it appears the same after rotation. So, the angle of rotation for a square is 90 degrees.

Order of Symmetry

The number of positions in which a figure can be rotated and still appears exactly like it did before the rotation, is called the order of symmetry. For example, a star can be rotated 5 times along its tip and look at same every time. Hence, its order of symmetry is 5.

Examples of Rotational Symmetry

• The recycle logo has an order of symmetry of 3.

• The paper windmill has an order of symmetry of 4.

• The triangle has an order of symmetry of 3.

• The Swastik symbol has an order of symmetry of 4.

• The roundabout road sign has an order of symmetry of 3.