# ORDER OF ROTATIONAL SYMMETRY

## About "Order of rotational symmetry"

Order of rotational symmetry - definition

The order of rotational symmetry is that an object has the number of times that it fits on to itself during a full rotation of 360 degrees.

## Order of rotational symmetry - Examples

To have better understanding on "order of rotational symmetry", let us look at some examples.

Example 1 :

What is the order of rotational-symmetry of an equilateral triangle ?

Solution :

As explained in the definition, we have to check, how many times an equilateral triangle fits on to itself during a full rotation of 360 degrees.

Please look at the images of the equilateral triangle in the order A,B and C. A is the original image. The images B and C are generated by rotating the original image A.

When we look at the above images of equilateral triangle, it fits on to itself 3 times during a full rotation of 360 degrees.

Hence, an equilateral triangle has rotational symmetry of order 3.

Let us look at the next example on "Order of rotational symmetry"

Example 2 :

What is the order of rotational-symmetry of a square ?

Solution :

As explained in the definition, we have to check, how many times a square fits on to itself during a full rotation of 360 degrees.

Please look at the images of the square in the order A, B, C, D and E. A is the original image. The images B, C, D and E are generated by rotating the original image A.

When we look at the above images of square, it fits on to itself 4 times during a full rotation of 360 degrees.

Hence, a square has rotational symmetry of order 4.

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Example 3 :

What is the order of rotational-symmetry of a regular pentagon ?

Solution :

As explained in the definition, we have to check, how many times a regular pentagon fits on to itself during a full rotation of 360 degrees.

Please look at the images of the regular pentagon in the order A, B, C, D, E and F. A is the original image. The images B, C, D, E and F are generated by rotating the original image A.

When we look at the above images of regular pentagon, it fits on to itself 5 times during a full rotation of 360 degrees.

Hence, a regular pentagon has rotational symmetry of order 5.

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Example 4 :

What is the order of rotational-symmetry of a parallelogram ?

Solution :

As explained in the definition, we have to check, how many times a parallelogram fits on to itself during a full rotation of 360 degrees.

Please look at the images of the parallelogram in the order A, B and  C. A is the original image. The images B and C are generated by rotating the original image A.

When we look at the above images of parallelogram, it fits on to itself 2 times during a full rotation of 360 degrees.

Hence, a parallelogram has rotational symmetry of order 2.

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Example 5 :

What is the order of rotational-symmetry of an isosceles triangle ?

Solution :

As explained in the definition, we have to check, how many times an isosceles triangle fits on to itself during a full rotation of 360 degrees.

Please look at the images of the isosceles triangle in the order A and B. A is the original image. The image B is generated by rotating the original image A.

When we look at the above images of isosceles triangle, it fits on to itself 1 time during a full rotation of 360 degrees.

Hence, an isosceles triangle has rotational symmetry of order 1.

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Example 6 :

What is the order of rotational-symmetry of an scalene triangle ?

Solution :

As explained in the definition, we have to check, how many times an scalene triangle fits on to itself during a full rotation of 360 degrees.

Please look at the images of the scalene triangle in the order A and B. A is the original image. The image B is generated by rotating the original image A.

When we look at the above images of isosceles triangle, it fits on to itself 1 time during a full rotation of 360 degrees.

Hence, a scalene triangle has rotational symmetry of order 1.

Let us look at the next example on "Order of rotational symmetry"

Example 7 :

What is the order of rotational-symmetry of a trapezium ?

Solution :

As explained in the definition, we have to check, how many times an trapezium fits on to itself during a full rotation of 360 degrees.

Please look at the images of the trapezium in the order A and B. A is the original image. The image B is generated by rotating the original image A.

When we look at the above images of trapezium, it fits on to itself 1 time during a full rotation of 360 degrees.

Hence, a trapezium has rotational symmetry of order 1.

Let us look at the next example on "Order of rotational symmetry"

Example 8 :

What is the order of rotational-symmetry of a isosceles trapezium ?

Solution :

As explained in the definition, we have to check, how many times an isosceles trapezium fits on to itself during a full rotation of 360 degrees.

Please look at the images of the isosceles trapezium in the order A and B. A is the original image. The image B is generated by rotating the original image A.

When we look at the above images of isosceles trapezium, it fits on to itself 1 time during a full rotation of 360 degrees.

Hence, an isosceles  trapezium has rotational symmetry of order 1.

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Example 9 :

What is the order of rotational-symmetry of a kite ?

Solution :

As explained in the definition, we have to check, how many times a kite fits on to itself during a full rotation of 360 degrees.

Please look at the images of the kite the order A and B. A is the original image. The image B is generated by rotating the original image A.

When we look at the above images of kite, it fits on to itself 1 time during a full rotation of 360 degrees.

Hence, a kite has rotational symmetry of order 1.

Let us look at the next example on "Order of rotational symmetry"

Example 10 :

What is the order of rotational-symmetry of a rhombus ?

Solution :

As explained in the definition, we have to check, how many times a rhombus fits on to itself during a full rotation of 360 degrees.

Please look at the images of the rhombus the order A, B and C. A is the original image. The images B and C are generated by rotating the original image A.

When we look at the above images of rhombus, it fits on to itself 2 time during a full rotation of 360 degrees.

Hence, a rhombus has rotational symmetry of order 2.

Let us look at the next example on "Order of rotational-symmetry"

Example 11 :

What is the order of rotational-symmetry of an ellipse ?

Solution :

As explained in the definition, we have to check, how many times an ellipse fits on to itself during a full rotation of 360 degrees.

Please look at the images of the ellipse the order A, B and C. A is the original image. The images B and C are generated by rotating the original image A.

When we look at the above images of ellipse, it fits on to itself 2 time during a full rotation of 360 degrees.

Hence, an ellipse has rotational symmetry of order 2.

Let us look at the next example on "Order of rotational-symmetry"

Example 12 :

What is the order of rotational-symmetry of a circle ?

Solution :

As explained in the definition, we have to check, how many times a circle fits on to itself during a full rotation of 360 degrees.

A circle has an infinite 'order of rotational symmetry'. In simplistic terms, a circle will always fit into its original outline, regardless of how many times it is rotated.

Hence, a circle has infinite order of rotational symmetry.

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