Rotational Symmetry Math Example 3

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Example 3

easy
A figure has rotational symmetry of order 44. List all angles of rotation that map it onto itself.

Solution

  1. 1
    Minimum angle: 360°4=90°\dfrac{360°}{4} = 90°.
  2. 2
    All angles are multiples of 90°90° up to 360°360°: 90°,180°,270°,360°90°, 180°, 270°, 360°.

Answer

90°, 180°, 270°, 360°90°,\ 180°,\ 270°,\ 360°
For a figure with rotational symmetry of order nn, the angles that map it to itself are all multiples of 360°n\frac{360°}{n} from that value up to and including 360°360°. The 360°360° rotation is always included as the identity.

About Rotational Symmetry

A figure has rotational symmetry if it looks identical after being rotated by some angle less than 360°360° about a central point. The order of rotational symmetry is the number of distinct positions where the figure looks the same during a full rotation.

Learn more about Rotational Symmetry →

More Rotational Symmetry Examples