What is the order of rotational symmetry for a circle?
A shape is said to have rotational symmetry if it looks the same in different positions when rotated about its centre. We can rotate a square by 90, 180 or 270 degrees and it will look exactly the same. So, the order of rotational symmetry of the square is 4. If a rectangle (which is not a square) is rotated it can be seen that a rectangle has rotational symmetry of order 2. Any shape, however strange, will have rotational symmetry of at least order 1 since there is one position where it looks the same! As Tom already said, a circle has rotational symmetry of infinite order. It doesn’t matter how much or how many times you rotate a circle about its centre, it will still look exactly the same. You can rotateit by 1 degree, or by 217, or by 12.5, or by 187.284735 degrees… basically for any number of degrees between 0 and 360, and we know there are infinitely many numbers between 0 and 360. Hope this helps.
