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:
“The words themselves are clean, so are the things to which they apply. But the mind drags in a filthy association, calls up some repulsive emotion. Well, then, cleanse the mind, that is the real job. It is the mind which is the Augean stables, not language.”
—D.H. (David Herbert)
“All of life and human relations have become so incomprehensibly complex that, when you think about it, it becomes terrifying and your heart stands still.”
—Anton Pavlovich Chekhov (1860–1904)
“In any case, raw aggression is thought to be the peculiar province of men, as nurturing is the peculiar province of women.... The psychologist Erik Erikson discovered that, while little girls playing with blocks generally create pleasant interior spaces and attractive entrances, little boys are inclined to pile up the blocks as high as they can and then watch them fall down: “the contemplation of ruins,” Erikson observes, “is a masculine specialty.””
—Joyce Carol Oates (b. 1938)