This is the second part of two posts about using ggplot to visualize geometric transformations in the complex plane.
Inversions For this post we’ll focus on inversions, having already covered rotations, translations, and reflections. An inversion can be thought of as a reflection across a circle, the the inside of the circle gets flipped to fill the plane outside the circle and the outside is flipped into the circle. This is a more complicated transformation, both to visualize and to perform mathematically, but is essential to geometry.
I’m currently teaching a Geometry course, and wished there was an easy way to illustrate geometric transformations for my students. I’m sure they’ll agree I’m not a great artist.
Since R is my preferred way to draw any picture, I thought “Let’s use GGPlot to show transformations!”
For those not versed in geometry, we would like to easily visualize translations (shifts along a vector), rotations, and dilations of points (or collections of points) in the complex plane.