In the sketch below you
see a circle withradius r
around point C.
Point P
is reflected
at this circle and its reflection
point is P'.
This reflection is called circle inversion.
Drag point
P and observe what happens to its reflection point P'
when P is inside, outside or on the circle's line.
A circle inversion is defined by the equation
CP⋅CP' = r2.
Move point P
to three different positions and check whether
the construction above satisfies this equation.
Reflecting a Circle at a Circle
In the following construction the red circle PQR is reflected at the black circle. The result of this reflection is the blue circle P'Q'R'.
Drag the red circle and observe its reflection, the blue circle.
What happens when the red circle passes through the center point C of the black circle?
Move points P, Q and R so that the red circle becomes a line. What is special about its reflection?
Constructing the Circle Inversion
You now know some important facts about the circle inversion that we
will need to construct the Pappus Chain in our frisbee. If you also want
to find out how to construct the circle inversion on paper have a look at
the web page about inversion byDavid E. Joyce.