`Definition of Circle`
` `
`Subject:      RE: Reply to "Do Points Have Area?"`
`Author:       Jesse Yoder jesse@flowresearch.com`
`Date:         Sat, 31 Jan 1998 12:59:34 -0500`
` `
`Hi DGoncz,`
` `
`I hope you have recovered from you long bout of sleeplessness.`
` `
`On Jan. 1, 1998, you wrote:`
` `
`        >"It is possible for a circle to consist only of four`
`> points. But it wouldn't be a conventional circle."`
`> `
`RESPONSE: I don't see how it's possible for a circle to consist of only`
`four points. This would not be a circle at all (even an unconventional`
`one), but simply four points that lie on a circle. `
` `
`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.`
` `
`I don't understand what you mean by saying "meaning can be ignored if`
`properties are specified." Since you mentioned this in a computer`
`context, are you talking about terms that have to intrinsic meaning, yet`
`have a function if the rules of their use are specified?`
` `
`Happy New Year to you as well!`
` `
`Jesse`

http://forum.swarthmore.edu/epigone/geometry-research/thyspenddwox/8E85093A9F04D11180BC00A0C92ABEAC144B39@arcmail.arcweb.com