Round is Beautiful

Consider a 2-dimensional circle. If we rotate the circle about its centre, at any angles we may wish, we still get a circle with a same final appearance like before. We may study the sphere as the next example and we are still able to get the same result. More interestingly for a sphere, the appearance remains the same even as we begin to change the angle of the axis of rotation.

Hence, we can simply state that the rotation of a circle through any angle is the same to any observer.

Such constancy in orientation actually allows the entire system to conserve all forces of nature in the Universe.

For the purpose of argument, we may test our analogy on objects such as a triangle or a square. A square needs 90 degrees to restore its original look while a triangle will need 120 degrees.

The dimension of a circle or a sphere is another interesting point to note. The circumference of a circle is given by 2pi.r, area is pi.r2 and the volume of the sphere is 4.pi.r3/3 where r is the radius from the centre. The common things is-their dimension is only dependent on one variable-radius-and they obey the constant pi. In other words, the change is size is directly proportional in the change in radius.