Difference between revisions of "Center"

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(rm equidistance on average)
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<small>This article is about the center of a geometric object.  For the center of a group, see [[Center (group theory)]].</small>
 
<small>This article is about the center of a geometric object.  For the center of a group, see [[Center (group theory)]].</small>
  
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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.
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The '''center''' of a [[circle]] is the point equidistant from all points of the circle. 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.  
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For example, all the points of a [[circle]] are equidistant from 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.  
 
  
 
The center of a [[square]] is not the same distance from every point on the square--the corners are further away from the center than the [[midpoint]]s of the sides. The center of a square is the point where the two [[diagonal]]s intersect.
 
The center of a [[square]] is not the same distance from every point on the square--the corners are further away from the center than the [[midpoint]]s of the sides. The center of a square is the point where the two [[diagonal]]s intersect.
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Figures like squares, [[triangle]]s, [[ellipse]]s, etc. are why we must say "on average" in the definition of "center". While not all points are the same distance away from the center of the figure, the distances will average to be the same value and cancel out.
 
  
 
For complicated geometric shapes and [[solid]]s, the term [[centroid]] is preferred.
 
For complicated geometric shapes and [[solid]]s, the term [[centroid]] is preferred.
  
 
[[Category:Geometry]]
 
[[Category:Geometry]]

Revision as of 14:41, August 7, 2009

This article is about the center of a geometric object. For the center of a group, see Center (group theory).

The center of a circle is the point equidistant from all points of the circle. 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.

The center of a square is not the same distance from every point on the square--the corners are further away from the center than the midpoints of the sides. The center of a square is the point where the two diagonals intersect.

For complicated geometric shapes and solids, the term centroid is preferred.

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