Rotational Symmetry

Samuel went to an exhibition and sat on a giant wheel.

Samuel comes back to his initial position after the completion of every round.

That is, after one complete rotation, the giant wheel comes back to its original position.

If an object looks the same after completion of full or part of a rotation,

Then we say that it has Rotational symmetry.

Let’s learn more about rotational symmetry.

During rotation, the size and shape of the object does not change.

Let’s take an example of a paper windmill that rotates around a fixed point.

The windmill looks exactly the same for each rotation of

The windmill looks the same at four positions in one complete rotation()

We say that this shape has rotational symmetry of order

Order of symmetry is the number of times an object looks same in a round of

The fixed point around which the object rotates is called the center of rotation.

The angle by which the object turns during the rotation is called the angle of rotation.

The angle of rotation for the windmill is

Let's solve few examples

Consider an equilateral triangle

The angle of symmetry for this triangle is

The triangle looks the same for in one complete rotation. So, the order of symmetry is

The center of rotation is the centroid of the equilateral triangle.

Consider a square

The angle of rotational symmetry for this square is

The square looks the same times in one complete rotation, the order of symmetry is

The centre of rotation is the centre of the square.

Consider a rectangle

The angle of rotational symmetry for the rectangle is

The rectangle looks the same times in one complete rotation, the order of symmetry is

The centre of rotation is the centre of the rectangle.

Consider a star named

The angle of rotational symmetry for this star is

The star looks the same times in one complete rotation, the order of symmetry is

The centre of rotation for this star is the centre of the star.

Revision

If an object looks the same after completion of full or part of a rotation,

Then we say that it has Rotational symmetry.

The fixed point around which an object rotates is called the center of rotation.

Order of symmetry is number of times an object looks the same in one complete rotation.

The angle by which the object turns during the rotation is called the angle of rotation.

The End