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Responding to SamHB's criticism of this article:

I'll agree this isn't the best written article. However, it has to have a definition that works for all plane figures, from circles to polygons and everything in between. Now there are easy definitions of center for some of these figures:
  • a circle's center is the unique point that is equidistant to every point on the circle.
  • a quadrilateral's center is the intersection of the two diagonals.
  • an ellipse's center is the intersection of the major and minor axes.
But even these three definitions alone are not easy to resolve into one that works in all cases. They also make strong use of the symmetry of the figures to get a simple definition. Throw in pentagons, hearts, stars, and strange figures such as cardioids, and the definition becomes more complicated. Basically, for this article I had to approach the formal definition of centroid while avoiding the use of integrals. That is to say, I had to explain the intuition of the integration involved in finding the centroid, which is not easy without actually writing an integral. Realizing that my "all-purpose" definition was somewhat hard to digest, I tried to clarify the definition with the examples of a circle and square.
It's ironic that I had to invoke the spirit of integration for the center article, since the centroid article should have been the more technical one. But the already-existing centroid article avoided integrals by referring to the term "center", so we've got a case of mathematical definitions by synonyms. I could have continued this trend by writing "the center of a geometric shape is the middle of the shape", but that's just avoiding the task of having to give a proper definition.
I welcome improvements to the article and constructive criticism. -Foxtrot 04:22, 28 August 2008 (EDT)
My question for Foxtrot: How can points be on average equidistant? What points do you take the average of? What do you want to say? IMO, this formulation is even less clear than "the center is in the middle"... --DiEb 13:47, 29 August 2008 (EDT)

Makes no Sense

I'm an occasional reader here and just noticed this page. As others seem to have noted, it doesn't make any sense. At all. However, I see it was edited by a couple sysops and I've seen what happens to editors here who disagree with them.
So, I will use my sole edit here to point out that this needs improvement. At least an attempt to explain what the center of a square is, using the definition "a point that, on average, the points of the shape are equidistant from." --AndyP 18:58, 27 November 2010 (EST)
Too bad you wasted it on such bull excrement, AndyP. I see two current Admins removing malarkey and the only other editor that was a sysop was removed for being an undercover liar from a well-known vandal site that specializes in CP. So much for your statement about "what happens" to those who disagree with Admins here. If I were to remove you it would be for shoddy posting, repeating what is untrue, which is sometimes the work of those very same vandal site members. I invite you to improve and make the article right. If you lack the ability to do so, I will delete it. Is that fair enough? --ṬK/Admin/Talk 19:15, 27 November 2010 (EST)
Fair enough. I think deletion is probably the best outcome in this case. --AndyP 19:21, 27 November 2010 (EST)