Inversive distance
Encyclopedia
Inversive distance is a way of measuring the "distance
" between two non-intersecting circle
s α and β. If α and β are inverted with respect to a circle centered at one of the limiting point
s of the pencil of α and β, then α and β will invert into concentric circles. If those concentric circles have radii a' and b' , then the inversive distance is defined as
In addition, if a and b are the radii of α and β (as opposed to their images), and c is the distance between their centers, then the inversive distance δ is given by
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...
" between two non-intersecting circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
s α and β. If α and β are inverted with respect to a circle centered at one of the limiting point
Limiting point
Limiting point has the following meanings in mathematics:*Limit*Limit point*Limiting point of coaxal circles...
s of the pencil of α and β, then α and β will invert into concentric circles. If those concentric circles have radii a
In addition, if a and b are the radii of α and β (as opposed to their images), and c is the distance between their centers, then the inversive distance δ is given by