Spacetime intervals may be classified into three distinct types, based on whether the temporal separation ({{math|''c''<sup>2</sup>Δ''t''<sup>2</sup>}}) or the spatial separation ({{math|Δ''r''<sup>2</sup>}}) of the two events is greater: time-like, light-like or space-like.
Certain types of [[world line]]s are called [[geodesic]]s of the spacetime – straight lines in the case of flat Minkowski spacespacetime and their closest equivalent in the curved spacetime of general relativity. In the case of purely time-like paths, geodesics are (locally) the paths of greatest separation (spacetime interval) as measured along the path between two events, whereas in Euclidean space and Riemannian manifolds, geodesics are paths of shortest distance between two points.<ref>This characterization is not universal: both the arcs between two points of a [[great circle]] on a sphere are geodesics.</ref><ref>{{cite book |title=Principles of Cosmology and Gravitation |first1=Michael V. |last1=Berry |publisher=[[CRC Press]] |year=1989 |isbn=0-85274-037-9 |page=58 |url=https://books.google.com/books?id=wTvFxXguod0C&pg=PA58}}</ref> The concept of geodesics becomes central in [[general relativity]], since geodesic motion may be thought of as "pure motion" ([[Fictitious force|inertial motion]]) in spacetime, that is, free from any external influences.
