Subject: RE: Reply to ""Reply to "Re: Do Points Have Area

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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