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Boundary Set

A (symmetrical) boundary set of Radius $r$ and center ${\bf x}_0$ is the set of all points ${\bf x}$ such that

\begin{displaymath}
\vert{\bf x}-{\bf x}_0\vert = r.
\end{displaymath}

Let ${\bf x}_0$ be the Origin. In $\Bbb{R}^1$, the boundary set is then the pair of points $x = r$ and $x = -r$. In $\Bbb{R}^2$, the boundary set is a Circle. In $\Bbb{R}^3$, the boundary set is a Sphere.

See also Circle, Disk, Open Set, Sphere




© 1996-9 Eric W. Weisstein
1999-05-26