The conventional geometry of our surrounding space is Euclidean. Strictly speaking, it is the geometry in a three-dimensional Euclidean space. If we restrict the geometry in a plane (e.g. the floor of a building) it turns out to be two dimensional Euclidean space. Again if a person is conservative enough to take into account of the curvature of earth, the 2-D planar floor is not strictly the Euclidean one. One may approximate it more accurately to the Riemannian space, which consists of the points lying on a spherical surface and the distances between two points are computed by the length of the arc defined by the circle with center and radius that are the same as those of the sphere.