Circle Inversion of Basic Figures

​
shape
circle
Explore the circle inversion of six figures. Drag the locators to move and scale the red pre-image. The blue shape is the image after circle inversion in the dashed circle.

Details

Inversion of a point
P
in a circle
C(A,r)
with center
A
and radius
r
to a point
Q
is the nonlinear mapping of the plane (except for the point
A
) to itself defined by
|AP|×|AQ|=
2
r
, where
A
,
P
, and
Q
are collinear. Inversion swaps the interior and exterior of
C
, preserves angles, and maps generalized circles to generalized circles. (A generalized circle is either an ordinary circle or a straight line.)

External Links

Inversion (Wolfram MathWorld)

Permanent Citation

Garrett Nelson, Branko Curgus
​
​"Circle Inversion of Basic Figures"​
​http://demonstrations.wolfram.com/CircleInversionOfBasicFigures/​
​Wolfram Demonstrations Project​
​Published: June 30, 2014