`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