endpoint
Endpoint
2006-07-22 07:49:40
2007-06-26 01:40:47
Definition
line segment
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An \emph{endpoint} of a line segment $L$ is a point that belongs to the boundary of $L$. Note that every line segment has two distinct endpoints. For example, if $V$ is a vector space and $a,b \in V$ with $b \neq 0$, then the endpoints of the line segment $\displaystyle L = \{ a+tb : t\in[0,1]\}$ are $a$ and $a+b$.
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\rput[a](4,-0.3){$a+b$}
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Note that the endpoints of the open line segment $\displaystyle L=\{a+tb:t\in(0,1)\}$ are also $a$ and $a+b$.
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\rput[a](4,-0.3){$a+b$}
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Endpoints can be defined in a \PMlinkescapetext{similar} manner for other geometric \PMlinkescapetext{objects}. These include rays, \PMlinkname{arcs}{PathConnected}, and \PMlinkname{intervals}{Interval}.
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\item Rays have one endpoint.
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\item \PMlinkescapetext{Arcs} have two endpoints.
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\item \PMlinkescapetext{Intervals} can have zero, one, or two endpoints, depending on whether they are bounded above and/or below. See the entry on \PMlinkname{intervals}{Interval} for more details.
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