In Real or Complex Vector Spaces
If V is a vector space over or, and L is a subset of V, then L is a line segment if L can be parameterized as
for some vectors, in which case the vectors u and u + v are called the end points of L.
Sometimes one needs to distinguish between "open" and "closed" line segments. Then one defines a closed line segment as above, and an open line segment as a subset L that can be parametrized as
for some vectors .
Equivalently, a line segment is the convex hull of two points. Thus, the line segment can be expressed as a convex combination of the segment's two end points.
In geometry, it is sometimes defined that a point B is between two other points A and C, if the distance AB added to the distance BC is equal to the distance AC. Thus in the line segment with endpoints A = (ax, ay) and C = (cx, cy) is the following collection of points:
- .
Read more about this topic: Line Segment
Famous quotes containing the words real, complex and/or spaces:
“Imaginary pains are by far the most real we suffer, since we feel a constant need for them and invent them because there is no way of doing without them.”
—E.M. Cioran (b. 1911)
“Instead of seeing society as a collection of clearly defined “interest groups,” society must be reconceptualized as a complex network of groups of interacting individuals whose membership and communication patterns are seldom confined to one such group alone.”
—Diana Crane (b. 1933)
“Deep down, the US, with its space, its technological refinement, its bluff good conscience, even in those spaces which it opens up for simulation, is the only remaining primitive society.”
—Jean Baudrillard (b. 1929)