Editing Line (geometry) (section)

=== Projective geometry ===
{{Further|Geodesic}}
[[File:Great circle hemispheres.png|right|thumb|A great circle divides the sphere in two equal hemispheres, while also satisfying the "no curvature" property.]]
In many models of [[projective geometry]], the representation of a line rarely conforms to the notion of the "straight curve" as it is visualised in Euclidean geometry. In [[elliptic geometry]] we see a typical example of this.<ref name=":0" />{{Rp|page=108}} In the spherical representation of elliptic geometry, lines are represented by [[great circle]]s of a sphere with diametrically opposite points identified. In a different model of elliptic geometry, lines are represented by Euclidean [[plane (geometry)|planes]] passing through the origin. Even though these representations are visually distinct, they satisfy all the properties (such as, two points determining a unique line) that make them suitable representations for lines in this geometry.

The "shortness" and "straightness" of a line, interpreted as the property that the [[distance]] along the line between any two of its points is minimized (see [[triangle inequality]]), can be generalized and leads to the concept of [[geodesic]]s in [[metric space]]s.