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Rotation Math

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In English, Rotation means to turn around an object around a center. When an object rotates around a centric Point then it is called as rotation. When any object rotates in three dimensional space about an imaginary line we call it as rotation. Just like this, we can give many definitions for a rotation. If we want to see the real world example of a rotation then we can take an example of earth. Earth revolves around the sun, this is also rotation. Moon revolves around the earth, it is also called rotation. Now the meaning of rotation is clear to you.

Now talk about the rotation in Math. In mathematics, when a rigid object revolves around the fixed point then it is called as rotation. It is just opposite of translation. We know that in translation the coordinates of an object changes and it moves from its origin to the destination location. When an object moves it could be either rotation or translation. When the object drags from one Position to another then it is translation and when is rotates around a fix point then it is rotation.

Rotational Symmetry

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A geometrical figure is in Rotational Symmetry, when we say that after rotating a figure by a certain angle, the figure looks same as before. Let us look at the Rotation Symmetry of an Equilateral Triangle. By rotating the equilateral triangle, we observe that the triangle looks exactly similar when it is rotated by 120 degrees, so the rotational symmetry will be at 120 degrees, 240 degrees and 360 degrees and then one rotation cycle is completed. Now, we come to the conclusion that a figure can look symmetrical 3 times when it completes one rotation. Thus, the order of rotation of the equilateral triangle will be 3.
On the other hand, if we look at the Isosceles Triangle or the Scalene Triangle, we observe that figure does not look same at any angular rotation, but after completing the rotation of 360 degrees it looks as it is. So the order of rotation is 1 and the angle of rotation is 360 degrees.
Have a look on another geometrical figure, say a Square. A square after the rotation of 90 degrees, take the exact shape, so the angle of the rotation of the square will be 90 degrees, 180 degrees, 270 degrees and 360 degrees. Thus we can say that the order of rotation of the square will be 4. Similarly, the order of rotation of the Rectangle will be 2 and the angle of rotation of the rectangle is 180 degrees.
Once we know the order of rotation of any figure, we can find the angle of rotation by applying the formula 360 / order of rotation.
By applying the same formula we say for equilateral triangle angle of rotation = 360 / 3 = 120 degrees.
For a square angle of rotation = 360 / 4 = 90 degrees and for the rectangle angle of rotation = 360 / 2 = 180 degrees.

Applications

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There are various application of rotation in math. Rotations math is also a type of transformation math. If coordinates are given then we can find the rotation from transformation.
Some instructions:
1: Point the coordinates on plane on x and y axis.
2: If we want to rotate the object 90 degree then just swap the x and y axis. And we will get new coordinates.
3: If we want to rotate 180 degree then there will be no swapping between x and y axis.
We have to change the positive axis into negative and negative to positive.
4: If we move the object 360 degree then we will be at the initial coordinates, there will be no change in any coordinate.