Definition of Circle
Subject: RE: Reply to "Do Points Have Area?"
Author: Jesse Yoder
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!



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