Inversive distance

Inversive distance (usually denoted as δ) is a way of measuring the "distance" between two non-intersecting circles α and β. If α and β are inverted with respect to a circle centered at one of the limiting points 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

$(\alpha ,\beta )=\left|\ln {\frac {a'}{b'}}\right|.$

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

$\cosh \delta =\left|{\frac {a^{2}+b^{2}-c^{2}}{2ab}}\right|.$

See also

• Coaxal circles
• Inversive geometry

References

• Coxeter, H. S. M. (1967). Geometry Revisited. Washington: MAA. ISBN 0-88385-619-0. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)