Page 206 - ICSE Math 7

Rotational symmetry

A figure is said to have rotational symmetry if it fits into itself more than once during a full turn,
i.e., rotation through 360°.
Let’s consider three blades of a fan marked A, B and C as shown in Fig. 1. Now, rotate the fan
about point O in clockwise direction. When the fan is rotated by 120° (i.e., 1/3 of 360°) the
blade A takes the position of blade B, blade B takes the position of blade C and blade C takes
the position of blade A (as shown in Fig. 2). We observe that Fig. 2 looks exactly the same as
the original Fig. 1. One more rotation through 120° brings the blade to a new position as shown
in Fig. 3. Finally after a third rotation by 120°, the blades of the fan come back to their original
position.

A C B A

120°
120°
O O O O O
C B A C B
B 120° A C

Fig. 1 Fig. 2 Fig. 3 Fig. 4

Thus in a full turn, there are precisely three positions (on rotation through the angles 120°,
240° and 360°) when the fan looks exactly the same. Because of this, one can claim that a fan
has a rotational symmetry of order 3. Now, we give a formal definition of order of rotational
symmetry.

Order of rotational symmetry
The number of times a figure looks exactly the same as its original shape in a complete turn (rotation
of 360°) is called the order of rotational symmetry.

360°
Thus, order of a rotational symmetry =

Example 5: Find the order of rotational symmetry and the angles of rotation of the following figures
about point O.

(a) O (b) O

Solution: (a) Order of rotational symmetry = 4
90°
360°
Smallest angle of rotation = = 90° 90° 90°
4
90°
\ Angles of rotation are 90°, 180° (90° + 90°),
270° (90° + 90° + 90°) and 360° (90° + 90° + 90° + 90°).

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