Let $n \in \mathbb{N}$, let $x_0 \in \mathbb{R}^n$, and let $r > 0$. Write $B(a,\rho) := \{z \in \mathbb{R}^n : |z-a| < \rho\}$ for the open Euclidean ball centered at $a \in \mathbb{R}^n$ with radius $\rho > 0$. Define the map $F: B(0,1) \to B(x_0,r)$ by $F(y) = x_0 + ry$. Then $F$ is a bijection, and its inverse is the map $G: B(x_0,r) \to B(0,1)$ defined by $G(x) = \frac{x-x_0}{r}$.