Inversjonssenter

Inversjonssenter is a geometric concept describing a specific type of transformation. When a point P is inverted with respect to a center C, the resulting point P' lies on the line passing through C and P. The distance from C to P' is the inverse of the distance from C to P, relative to a chosen inversion radius. Mathematically, if C is the origin (0,0) and P has coordinates (x, y), then P' has coordinates proportional to (x, y) such that the product of the distances CP and CP' equals the square of the inversion radius, r^2. In 2D, this can be expressed as P' = (r^2 * x) / (x^2 + y^2), (r^2 * y) / (x^2 + y^2).

Inversion with respect to a center can transform geometric objects in unique ways. Lines not passing through the center of inversion are mapped to circles passing through the center. Lines passing through the center are mapped to themselves. Circles not passing through the center are mapped to other circles not passing through the center. Circles passing through the center are mapped to lines not passing through the center. This transformation is particularly useful in certain areas of geometry, such as inversive geometry and circle packing problems, offering alternative perspectives and simplifying complex configurations.