Inverse Geometry

We can develop a mapping of the plane where all points external to a circle

--  Where all points outside a given circle are mapped to points inside the circle

--    Where all points inside the given circle are mapped to points outside the circle

--    Where points on the circle are mapped onto themselves

There is usually no loss of generality to take the circle of inversion to have a radius of  r = 1 and so the inverse relationship is given.



Click here for a GSP script tool to implement the mapping.

1.   Use the  inversion ideas to construct a trisection of a line segment.

2.   Develop an inversion procedure for dividing a segment into   n   equal segments.

3.   Show that the inversion a circle that does not go through the center of the inversion circle is another circle.    Describe the different possibilities.

4.   Show that the inversion of a circle passing through the center of the circle of inversion will have an image that is a line.   Describe.

5.    Find the images of other curves or figures.

To be continued.