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Do Points
Have Area? Definition of Circle Subject: RE: Reply to "Do Points Have Area?" Author: Jesse Yoder jesse@flowresearch.com Date: Sat, 31 Jan 1998 12:59:34 -0500 Hi DGoncz, I hope you have recovered from you long bout of sleeplessness. On Jan. 1, 1998, you wrote: >"It is possible for a circle to consist only of four > points. But it wouldn't be a conventional circle." > RESPONSE: I don't see how it's possible for a circle to consist of only four points. This would not be a circle at all (even an unconventional one), but simply four points that lie on a circle. A circle by its very nature (in other words, by definition), is a continuous circular line. This is what's wrong with the traditional definition of a circle as "a set of points equidistant from a fixed point." If these points aren't "continuous", there is no circle, but merely a set of points arranged in a circular fashion. I believe that the Euclidean tendency to identify a line with "infinitely many points" tends to obscure the requirement that the points lying on a circle must be continuous in order for a circle to exist. I don't understand what you mean by saying "meaning can be ignored if properties are specified." Since you mentioned this in a computer context, are you talking about terms that have to intrinsic meaning, yet have a function if the rules of their use are specified? Happy New Year to you as well! Jesse
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