# Definition(s) > [!NOTE] Definition 1 (Spherical Line/ Great Circle) > Let $n$ be any natural number. A great circle on the [[n-Sphere|n-sphere]] $S_{r}^n$ is any subset of the form $S_{r}^n \cap V$where $V\subset \mathbb{R}^{n+1}$ is a [[Dimension of Finite Dimensional Real Vector Space|2-dimensional]] [[Subspace of Real n-Space|vector subspace]] of $\mathbb{R}^{n+1}.$ > [!Example] Example > Contents # Properties(s) # Application(s) **More examples**: # Bibliography