Difference between revisions of "Center"

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(remove drivel)
(not at all drivel. reinstate and clarify with example of square)
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The '''center''' of a [[circle]] is the point that all the points on the curve are equidistant from. The center is not a point on the circle because the circle is only the rim and has empty interior.  
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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.  
  
In contrast, the center of a disk is a point of the disk. See [[centroid]].
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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.  
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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.
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For complicated geometric shapes and [[solid]]s, the term [[centroid]] is prefered.
  
 
[[Category:Geometry]]
 
[[Category:Geometry]]

Revision as of 19:15, 15 January 2009

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.

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.

Figures like squares, triangles, ellipses, 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 solids, the term centroid is prefered.