CLASS-7
GEOMETRY - SYMMETRY - ROTATION

SYMMETRY - ROTATION -

Rotational Symmetry occurs when a shape or object looks the same after being rotated around a central point by a certain angle. If you can rotate the shape less than a full circle (360°) and it still matches its original appearance, the shape has rotational symmetry.

Key Features of Rotational Symmetry:-

  • Center of Rotation:- The point around which the shape is rotated.
  • Angle of Rotation:- The smallest angle through which a shape can be rotated to look the same.
  • Order of Rotation:- The number of times the shape looks identical during a full 360° rotation.


Order of Rotation:-

The order of rotation refers to how many times a shape looks exactly the same within one full turn (360°).

                                 360∘

 Order of Rotation = -------------------

                           Angle of Rotation


Examples of Rotational Symmetry:-

   1. Geometric Shapes:-

      (a) Equilateral Triangle:- Rotational symmetry of order 3 (matches every 120° rotation).

      (b) Square:- Rotational symmetry of order 4 (matches every 90° rotation).

      (c) Circle:- Infinite order of rotation (looks the same at any angle).


   2. Letters and Numbers:-

      (a) Letters:- The letters H, N, O, S, Z exhibit rotational symmetry.

      (b) Numbers:- The number 8 has rotational symmetry of order 2 (matches at 180° and 360°).


   3. Natural Objects:-

      (a) Flower petals:- Many flowers, such as daffodils, have rotational symmetry.

      (b) Starfish:- A starfish with 5 arms has rotational symmetry of order 5 (72° rotations).


   4. Objects and Patterns:-

     (a) Propellers:- Rotational symmetry ensures the blades are evenly balanced.

     (b) Fidget spinners:- These objects exhibit rotational symmetry, which gives them smooth spinning behavior.


Real-Life Applications of Rotational Symmetry:-

  • Wheels and Gears:- Rotational symmetry ensures smooth and balanced motion.
  • Design and Logos:- Many logos (e.g., Mercedes-Benz) use rotational symmetry for aesthetic appeal.
  • Art and Architecture:- Mandalas and circular patterns often incorporate rotational symmetry to create harmony.