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Do Points
Have Area? Definition of Circle Subject: REPLY TO "RE: REPLY TO POINTS HAVE AREA?" Author: CANDICE HEBDEN <DREAMY_AURORA@hotmail.com> Date: 1 Feb 98 18:35:13 -0500 (EST) JESSE--- [YOU WROTE ON JANUARY 31, 1998] >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. RESPONSE: WHERE DID YOU EVER READ THAT A CIRCULAR HAD TO BE A CONTINUOUS CIRCULAR LINE??? DEPENDING ON WHAT FORM OF GEOMETRY YOU'RE USING, A CIRCLE COULD CONSIST OF FOUR POINTS. IF YOU WERE TO HAVE TAXICAB GEOMETRY WHERE POINTS COULD ONLY EXIST ON THE "CORNERS", THEN, IF YOU USE EUCLIDEAN'S DEFINITION OF A CIRCLE (ALL POINTS EQUIDISTENT FROM A FIXED POINT), YOU GET A CIRCLE THAT CONSISTS OF FOUR POINTS. HOPE TO TALK TO YOU LATER JESSE, CANDICE HEBDEN @ DREAMY_AURORA@HOTMAIL.COM
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