Wilson Stothers' Inversive Geometry and CabriJava Pages

The object of these pages is to introduce inversive geometry.
Many of the results and ideas are Greek, largely due to Apollonius of Perga

We shall approach from the Klein viewpoint, that is to say using a
group of transformations of a set of points.

To motivate the definitions of the set and its transformations,
we begin by looking at a classical greek Theorem (Apollonius's Theorem).

Whenever it is useful, we give CabriJava (interactive) illustrations.
For example, the CabriJava pane on the right shows three touching red circles.
The blue and green circles each touch all of the red circles.
By dragging A or B, you can change the red circles, but it is always possible
to draw the blue and green circles.

Why? That's what inversive geometry is about.
You can find an inversive proof here.

table of contents

• Apollonian Families
• The basic properties of inversion
• The extended plane and i-lines
• The Equal Angles Theorem
• The Inversion Theorem and i-lines
• The Invariance of Angle
• Orthogonal Curves
• The Algebraic Inversion Theorem
• The Interior-Exterior Theorem
• More about Apollonian Families
• Steiner's Porism
• The Arbelos
• The Problem of Apollonius
• more on orthogonal i-lines