Rotational Symmetry Math Example 2

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Example 2

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Which of the letters 'S' and 'H' has rotational symmetry? State the order and angle for each that qualifies.

Solution

  1. 1
    Test 'S': Rotate 180°180° about its center — the shape looks the same. So 'S' has rotational symmetry of order 22, angle 180°180°.
  2. 2
    Test 'H': Rotate 180°180° about its center — the two vertical bars swap and the crossbar stays centred, so 'H' looks the same. 'H' also has rotational symmetry of order 22, angle 180°180°.
  3. 3
    Neither 'S' nor 'H' returns to itself after a 90°90° or 120°120° rotation, so their order is exactly 22.

Answer

Both 'S' and 'H' have rotational symmetry of order 22 (angle 180°180°).
Rotational symmetry exists whenever a figure looks identical after rotating less than 360°360°. Many letters have 180°180° (point) symmetry, meaning they are unchanged when rotated halfway around their centre.

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