Rotational Symmetry Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumWhich of the letters 'S' and 'H' has rotational symmetry? State the order and angle for each that qualifies.
Solution
- 1 Test 'S': Rotate about its center — the shape looks the same. So 'S' has rotational symmetry of order , angle .
- 2 Test 'H': Rotate 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 , angle .
- 3 Neither 'S' nor 'H' returns to itself after a or rotation, so their order is exactly .
Answer
Both 'S' and 'H' have rotational symmetry of order (angle ).
Rotational symmetry exists whenever a figure looks identical after rotating less than . Many letters have (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 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
Example 1 easy
Determine the order of rotational symmetry and the minimum angle of rotation for a regular hexagon.
Example 3 easyA figure has rotational symmetry of order [formula]. List all angles of rotation that map it onto it
Example 4 mediumEquilateral triangle [formula] is centred at the origin. A [formula] counterclockwise rotation maps