If an object retains the original shape when transformed, it is said to have symmetry. For example a vertical parabola when flipped across the vertical line passing through the vertex, it retains its shape. So we call that a vertical parabola is symmetrical over the axis through the vertex which is also called as axis of symmetry of the parabola.
Same way if an object retains the original shape when rotated over the center of the object by certain angle, it is said to have a rotational symmetry. It is also called as angular symmetry. This concept is dealt in the topic of rotational symmetry definition geometry. Let us take a closer look.
In real life there are many examples of rotational-symmetry. For example, a fan with certain number of blades has an angular symmetry because the angle between any two consecutive blades is constant. Rotating the blade by that much of angle we can observe that the shape of the fan appears to be same as it was originally.
In the above example, it was fairly easier to observe the angular symmetry. But, in general, how to find rotational symmetry? One has to keenly note that if the given shape looks same as before even when undergoes the transformation of rotation by some angle.
In certain cases, the original shape is retained repeatedly. That is, before completing one full revolution, the shape exhibits the originality a number of times. This ‘number of times’, is known as order of rotational symmetry of the shape. Consider an equilateral triangle. The shape remains the same after every rotation of 120o and hence in one complete revolution the shape of the equilateral triangle remains the same three times. Therefore, the order here of the angular symmetry in this case is 1. A square has that order as 4 whereas a rectangle has only two. A circle has the same order infinitely.
Now let us discuss an important point. An object comes back to the original shape only when it undergoes a complete rotation. Can we say that 1 is the order of angular symmetry for this object? No! A rotational symmetry for any object is said to exist only when it exhibits the original shape more than once in one complete revolution. For that matter, all the objects come back to the original shape after a rotation of 360o. Therefore, 1 as the order of angular symmetry does not exist and also it does not make sense. Thus, the minimum order for an angular symmetry is 2.
Same way if an object retains the original shape when rotated over the center of the object by certain angle, it is said to have a rotational symmetry. It is also called as angular symmetry. This concept is dealt in the topic of rotational symmetry definition geometry. Let us take a closer look.
In real life there are many examples of rotational-symmetry. For example, a fan with certain number of blades has an angular symmetry because the angle between any two consecutive blades is constant. Rotating the blade by that much of angle we can observe that the shape of the fan appears to be same as it was originally.
In the above example, it was fairly easier to observe the angular symmetry. But, in general, how to find rotational symmetry? One has to keenly note that if the given shape looks same as before even when undergoes the transformation of rotation by some angle.
In certain cases, the original shape is retained repeatedly. That is, before completing one full revolution, the shape exhibits the originality a number of times. This ‘number of times’, is known as order of rotational symmetry of the shape. Consider an equilateral triangle. The shape remains the same after every rotation of 120o and hence in one complete revolution the shape of the equilateral triangle remains the same three times. Therefore, the order here of the angular symmetry in this case is 1. A square has that order as 4 whereas a rectangle has only two. A circle has the same order infinitely.
Now let us discuss an important point. An object comes back to the original shape only when it undergoes a complete rotation. Can we say that 1 is the order of angular symmetry for this object? No! A rotational symmetry for any object is said to exist only when it exhibits the original shape more than once in one complete revolution. For that matter, all the objects come back to the original shape after a rotation of 360o. Therefore, 1 as the order of angular symmetry does not exist and also it does not make sense. Thus, the minimum order for an angular symmetry is 2.
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