Pyörähdyssymmetrisyys

Pyörähdyssymmetrisyys, known in English as rotational symmetry, describes a property of a shape or object where it appears identical after being rotated by some amount around a central point. The degree of symmetry is determined by the number of times the object can be rotated by less than a full 360 degrees and still appear the same. This number is called the order of rotational symmetry. For example, a square has rotational symmetry of order 4, as it can be rotated by 90, 180, and 270 degrees to look identical to its original position. A circle possesses infinite rotational symmetry, as it looks the same after any rotation around its center.

The angle of rotation required to return the object to its original orientation is found by dividing 360 degrees by the order of symmetry. So, for the square, 360/4 = 90 degrees. An object with rotational symmetry of order 1 only appears the same after a full 360-degree rotation, which is true for any object, and therefore is not typically considered to have significant rotational symmetry. Many natural phenomena and man-made designs exhibit pyörähdyssymmetrisyys, including snowflakes, starfish, pinwheels, and the arrangement of petals in many flowers. The concept is fundamental in geometry and is applied in fields such as crystallography, art, and design to describe and analyze patterns.