Spherical Geometry according to Klein is the pair \((S^{n-1},\,\mathrm {O}(n))\) . Spherical Geometry deals with the properties and relationships of points, lines, and shapes located on the surface of the unit sphere \(S^{n-1}\) of \({{\mathbb R}}^n\) . In contrast to Euclidean Geometry, whose environment is flat, in Spherical Geometry we focus on figures like those encountered in geography and astronomy. One of the fundamental characteristics of Spherical Geometry is that its “straight lines” are great circles, meaning circles with radius 1 centered at the centre of \(S^{n-1}\) . These great circles play the role of straight lines in Euclidean Geometry. A tangible example is that of the meridians and parallels of the Earth: the former are great circles while the latter are minor circles, meaning their centre (except for the Equator) is not the centre of the Earth.