Week 4

Inversions of disks are reflections in the Minkowski space!

$$\hbox{Ref}_{\mu(K)} \mu(D) \ = \ \mu\left( \hbox{Inv}_K \, D\right)$$

Simply:

$$\hbox{Inv}_K \, D = D+2\langle K,D\rangle \, K$$ where $D$ is a disk (vector) and $K$ is a circle through which the disk is inverted.

Mini-challage:  Find the matrix representation of the inversion through $K$ and show it is a Lorentz transformation (belongs to $O(1,3)$).

A quick introduction to inversions in 2D (classical geometry).