Center
This is an old revision of this page, as edited by Foxtrot (talk | contribs) at 12:16, July 17, 2008. It may differ significantly from current revision.
The center of a geometric shape is a point that, on average, the points of the shape are equidistant from. This point does not have to be on the shape itself.
For example, all the points of a circle are equidistant the center, however the center is not a point on the circle because the circle is only the rim and has empty interior. In contrast, the center of a disk is a point of the disk.
We must say "on average" in the definition because, for example, not all points are the same distance away from the center of a square, however the distances will average to be the same value and cancel out.
For complicated geometric shapes and solids, the term centroid is prefered.