Symmetry and Transformations (2/4)

 1. General Information 2. Translation 3. Rotation 4. Reflection 5. Glide Reflection 6. Hands-On Activities
Rotations and Rotational Symmetry
Another type of symmetry is rotational symmetry. Rotational symmetry results from the transformation called rotation.

Rotation is the turning of a shape around a center point called the center of rotation. The distance to the center of rotation is kept constant. The amount of turning called the angle of rotation and is measured in degrees.

 A simple rotation of a point (red) to form another point (blue). Notice that the distances from the points to the center of rotation remain the same.

Here are two examples of rotations applied to entire shapes, not just a single point. The original shape together with its rotated copies is said to have rotational symmetry.

 Here are two examples of rotation. On the left, the "P" is being turned around the red dot 60 degrees each time. On the right, the polygon is being turned around the red dot 90 degrees each time.

Finally, what does it mean for a tessellation to have rotational symmetry? If we can perform a rotation to a tessellation that such that the result is the same as the original tessellation, then the tessellation has rotational symmetry. An example is as follows:

 This tessellation has rotational symmetry. After rotation around the red point through a certain number of degrees (60 to be exact), you find that the copy exactly matches the original.

 Real examples of rotational symmetry:

 After trying the hands-on activity, use the templates on the templates page to see why every regular, semiregular, and demiregular tessellations has rotational symmetry. Use the technique that was explained in the hands-on activity.