Directed line segment

Directed line segment

When a line segment is given an orientation (direction) it is called a directed line segment or oriented line segment. It suggests a translation or displacement (perhaps caused by a force). The magnitude and direction are indicative of a potential change. Extending a directed line segment semi-infinitely produces a directed half-line and infinitely in both directions produces a directed line. This suggestion has been absorbed into mathematical physics through the concept of a Euclidean vector. The collection of all directed line segments is usually reduced by making equipollent any pair having the same length and orientation. This application of an equivalence relation was introduced by Giusto Bellavitis in 1835.