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1-ball : ウィキペディア英語版
Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its end points. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints.
Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or otherwise a diagonal. When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve).
==In real or complex vector spaces==
If ''V'' is a vector space over \mathbb or \mathbb, and ''L'' is a subset of ''V'', then ''L'' is a line segment if ''L'' can be parameterized as
:L = \ \mid t\in()\}
for some vectors \mathbf, \mathbf \in V\,\!, in which case the vectors u and 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
: L = \ \mid t\in(0,1)\}
for some vectors \mathbf, \mathbf \in V\,\!.
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 \mathbb^2 the line segment with endpoints and is the following collection of points:
:\ = \sqrt\}.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Line segment」の詳細全文を読む



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