punktsümmeetria

Punktsümmeetria, also known as point symmetry or central symmetry, is a geometric concept describing a type of symmetry where an object can be rotated 180 degrees around a central point and appear unchanged. This central point is referred to as the center of symmetry. If a shape possesses point symmetry, every point on the shape has a corresponding point on the opposite side of the center of symmetry, equidistant from it.

For any point P on the object, its corresponding point P' will lie on the line passing through the center of symmetry C. The distance from C to P will be equal to the distance from C to P'. Mathematically, if C is the origin (0,0) and P has coordinates (x,y), then its symmetric point P' will have coordinates (-x,-y).

Examples of objects with point symmetry include a rectangle, a circle, a parallelogram, and the letter 'S' or 'Z'. In three dimensions, a sphere or a cube exhibits point symmetry. Many organic and inorganic molecules also display point symmetry. Understanding point symmetry is crucial in fields such as geometry, crystallography, and chemistry for analyzing the structure and properties of various objects and substances. It's a fundamental transformation that preserves the shape and size of an object while altering its orientation.