Does it Look the Same?


You must have heard the word rotation a number of times, the most common being the rotation of Earth. But did you know that rotation by an object is related to its symmetry as well? The chapter below shall let you know how the rotation is related to an objects symmetry.

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It is the movement of an object around its own axis. The motion of Earth around its own axis is the most common example. Now, what does rotation have to do with symmetry? Almost every object can rotate on its axis or on a fixed point, but is the shape same as the original after rotation? Yes, this is what we shall study in the chapter.


Earth rotates, and after every interval of turn, its shape is the same as on its original position. This means that Earth follows the principle of rotation symmetry. The axis of Earth here is the line of symmetry, which lets us know the change in position. Another example is the windmill. After every small turn, the shape of the windmill seems to be similar to that of its original position.

Also called as the radial symmetry, rotational symmetry finds use in many areas of Mathematics, Biology, and Physics. It can be defined as the state when the object’s shape is the same after a partial turn or any instance of rotation. The degree denotes the number of varying orientations in which the objects looks the same as it looked before rotating.

Number of Turns and Symmetry

Rotational symmetry depends on the number of turns and the outcome of such turns as well. Since rotation is a circular motion of the object around its own axis, the object follows a set of turns to reach back its original position. During this circular motion, an object undergoes half turn and one-fourth turn. If the shape of the object after these turns matches the shape of the object at the original position then it is said that the object is rotationally symmetrical.


Angle of Rotation

The angle of turn during the rotational movement of the object is the angle of rotation for the same object. Let’s take a pentagon for example. If a pentagon is rotated by 72 °, the shape of the Pentagon appears to be the same after the rotation, 72° shall be the angle of rotation for the Pentagon.

Center of Rotation

The point around which the rotation takes place is called the center of rotation. This point is fixed and the object rotates around it.

Solved Question for You

Question 1. Give a few more examples of shapes and things in nature that show rotational symmetry, apart from the once discussed in the chapter above?

Answer : Shapes that show rotational symmetry: Square, Rhombus, Equilateral Triangle, Hexagon and many more. Natural things that show rotational symmetry: Starfish, Flower, Sliced part of Lady’s finger etc.

Question 2 : All figures when rotated come back to its original position. The angle of rotation is

  1. 90º
  2. 180º
  3. 270º
  4. 360º

Answer : D. One complete revolution is equivalent to the circular path. Therefore the total angle is 360º.

Question 3: What do you mean by rotation?

Answer: Rotation refers to the movement of an object or thing around the center or point of rotation. E.g. the rotation of the earth around the sun is known as a revolution or orbital revolution. In simple words, rotation refers to the movement of an object in a circular path.

Question 4: What is the rotation in math?

Answer: In mathematics, rotation refers to the transformation that turns a figure about a fixed point called the center of rotation. Moreover, an object and its rotation are the same shape and size; however, the figures may be turned in different directions. In addition, rotation can be counter-clockwise or clockwise.

Question 5: Which things do not change after rotation?

Answer: After completion of rotation angle measures, shapes, the position of the center, and sizes do not change.  Furthermore, rotation is a solid transformation that rotates a geometric shape in a clockwise and counter-clockwise direction around a fixed center point and given angle.

Question 6: Explain clockwise and counter-clockwise rotation?

Answer: Clockwise rotation refers to the movement of the object along with the movement of the clock means from right to left. On the other hand, the counter-clockwise movement is just the opposite of clockwise movement means from left to right.

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