#
Inversive Circles

Pure Mathematics Department, University of Waterloo, Ontario, Canada

### Three examples of sets of inversive circles

### A chain of four touching circles inverted in each other

### Four mutually touching circles inverted in each other

### A chain of five touching circles inverted in each other

##
Description

These images are all produced from recursive PostScript programs.
They are all formed by repeatedly inverting one circle in another circle.
The code below shows how to find the inverse of a point in a circle.
More code can be found by looking at the complete PostScript file of the first image.
###
PostScript Function to Invert a Point in a Circle

/invertPoint
{%def Invert point xp yp in circle xc yc rc
%stack before: xc yc rc xp yp
/yp exch def
/xp exch def
/rc exch def
/yc exch def
/xc exch def
/xp xp xc sub def
/yp yp yc sub def
rc dup mul
xp dup mul
yp dup mul add
div dup %rc^2/(xp-xc)^2+(yp-yc)^2
xp mul
xc add %xinvpoint
exch
yp mul
yc add %yinvpoint
%stack after: xinvpoint yinvpoint
} def

© 1997 by William Gilbert
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This page was last updated on
February 21, 2008