Line segment: Difference between revisions

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{{Short description|Part of a line that is bounded by two distinct end points; line with two endpoints}}

[[Image:Segment definition.svg|thumb|250px|right|The geometric definition of a closed line segment: the [[intersection (Euclidean geometry)|intersection]] of all points at or to the right of {{mvar|A}} with all points at or to the left of {{mvar|B}}]]

[[File:Fotothek df tg 0003359 Geometrie ^ Konstruktion ^ Strecke ^ Messinstrument.jpg|thumb|Historical image of 1699 - creating a line segment]]

{{General geometry}}

In [[geometry]], a '''line segment''' is a part of a [[line (mathematics)|straight line]] that is bounded by two distinct end'''endpoints''' (its [[Pointextreme (geometry)|pointspoint]]s), and contains every [[Point (geometry)|point]] on the line that is between its endpoints. It is a special case of an ''[[arc (geometry)|arc]]'', with zero [[curvature]]. The [[length]] of a line segment is given by the [[Euclidean distance]] between its endpoints. 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. In [[geometry]], a line segment is often denoted using an [[overline]] ([[vinculum (symbol)|vinculum]]) above the symbols for the two endpoints, such as in {{mvar|{{overline|AB}}}}.<ref>{{Cite web|title=Line Segment Definition - Math Open Reference|url=https://www.mathopenref.com/linesegment.html|access-date=2020-09-01|website=www.mathopenref.com}}</ref>

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 (geometry)|edge]] (of that polygon or polyhedron) if they are adjacent vertices, or a [[diagonal]]. When the end points both lie on a [[curve]] (such as a [[circle]]), a line segment is called a [[chord (geometry)|chord]] (of that curve).

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==As a degenerate ellipse==

A line segment can be viewed as a [[Degenerate conic|degenerate case]] of an [[Ellipse#Line segment as a type of degenerate ellipse|ellipse]], in which the semiminor axis goes to zero, the [[Focus (geometry)|foci]] go to the endpoints, and the eccentricity goes to one. A standard definition of an ellipse is the set of points for which the sum of a point's distances to two [[focus (geometry)|foci]] is a constant; if this constant equals the distance between the foci, the line segment is the result. A complete orbit of this ellipse traverses the line segment twice. As a degenerate orbit, this is a [[Elliptic orbit#Radial elliptic trajectory|radial elliptic trajectory]].

==In other geometric shapes==

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==External links==

{{commons|Line segment|Line segment}}

{{Wiktionary|line segment}}

*{{mathworld |urlname=LineSegment |title=Line segment }}