Inversion Development
These are the html java applets for the talk:
Getting a Definition
Starting with a look at the reflection transformation, we develop a
definition of a transformation of (a punctured) plane based on a circle.
- Reflections: a reminder of a
distance perserving transformation.
- Revisiting Reflections: a new
characteriztion to motivate inversion in a circle.
- A "new
construction" for a reflection: a new
characteriztion to motivate inversion in a circle.
- Looking for inversion:
using the reflection model on a circle.
- Why P doesn't matter: just as in the line
example, A' is independent of our choice for P.
- More why P doesn't matter: just as in the line
example, A' is independent of our choice for P.
Having a definition, we look at ways to construct the transformation.
- Characterizing a circle:
looking at different locus characterizations for a circle.
- Constructing a tangent from a
point to a circle: we'll use this to ge an easy compass and
straight-edge construction of an inversion.
- Another construction of an
inversion:
- A compass only construction of an inverse
point: Just for fun.
Playing with the Definition
Having the definition and constructions, we explore inversions of lines and
circles.
- inversion on a the circle of
inversion
- inversion on a line through the
center of inversion
- inversion
on a point on a line (not through the
center of inversion)
- Inverting a line (not through O)
- inversion
on a point on a circle
- inversion of a circle
- Inversion and Similar Triangles
- Proving inverting a line (not through
O)
- Revisit inverting concentric
circles
Steiner's Alternative