Stereographic projection \[\sigma: \mathbb{R}^n \to S^n \setminus \{\mathbf{n}\}\] where \[\mathbf{n}=(0,\ldots,0,1)\in\mathbb{R}^{n+1}\] is the northpole of $S^n$ is a special case of an inversion: Let us consider the hypersphere $S\subset\mathbb{R}^{n+1}$ with center $\mathbf{n}$ and radius $r=\sqrt{2}$ and look at the image of \[\mathbb{R}^n =\left\{\mathbf{x}\in\mathbb{R}^{n+1}\,{\large … Continue reading Conformal Maps III: Stereographic Projection