Definition of Circle

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

http://forum.swarthmore.edu/epigone/geometry-research/thyspenddwox/sp7yz32axrxy@forum.swarthmore.edu