Measuring Points
Subject: RE: Reply to ""Reply to "Re: Do Points Have Area?""
Author: Jesse Yoder jesse@flowresearch.com
Date: Mon, 2 Feb 1998 16:50:30 -0500
Hey Candice - Sorry I overlooked this email. Let me respond to your
questions.
You wrote:
> In respect to your Points, when you measure the distance between two
> Points, do you measure from???
>
> a. the center of the two points,
> b. from the sides facing each other, or
> c. from the opposite sides?
>
RESPONSE: In general, I would say "Use corresponding positions. So if
you measure from the center of Point A, use the center of point B. Your
choices b and c violate this principle. This is a real-world problem
that most people completely ignore.
> If your answer is a, how can you have a center to the smallest
> circular mesurement??? Wouldn't that center have to be at a Point???
> So then the center of a Point is a Point which is a Point to infinity!
>
RESPONSE: I know (or believe) you are trying to find a contradiction in
my theory here. What I have said is that a Point is the smallest unit of
measurement accepted for a given purpose or application. So you are
treating the Point as being "unbreakable" for your measurement. So in a
sense the distance between any two Points A and B is from anyplace on A
to anyplace on B. But logic would dictate using corresponding locations
on A and B, and measuring from there.
Your discussions of b and c are interesting, but I reject both of these
as answers.
> If your answer is b, how can you have area that doesn't exist???
>
> Because if you want to find the length between Point A and Point B,
> and there exists a Point C (which is colinear with A and B) which is
> between Point A and Point B. Because AC+CB=AB when the points are
> colinear, we must account for the length in Point C... which is not
> measured with AC or with CB, so then, in your circular geometry, AC +
> CB does not equal AB. AC + CB < AB
>
> If your answer is c, how can you count up area twice... in the
> above
> scenario with this answer, AC + CB > AB
>
>
Jesse
http://forum.swarthmore.edu/epigone/geometry-research/smumshenskel
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