Line is a Circle

Gordon · 30-04-2003 08:51PM

lol

Let me guess... Good Will Hunting is somewhere in this thread... 0_o

CuLT · 30-04-2003 09:58PM

Sev · 30-04-2003 10:40PM

Originally posted by bonkey
b) They do intersect, in which case the lines were not parallell, unless we stated we were dealing with a curved space, in which case there is no question - lines are arcs.

Couldn't parallel lines be considered to intersect at infinity?

ecksor · 30-04-2003 10:44PM

Originally posted by Sev
Couldn't parallel lines be considered to intersect at infinity?

No, the definition of parallel lines are lines that do not intersect.

Gordon · 30-04-2003 10:46PM

Originally posted by Sev
Couldn't parallel lines be considered to intersect at infinity?

Sev, I'm no maths genius, I used to be when I was 14 but it all got way over my beer belly after that. But, no parallel lines never intersect, sorry.

Sev · 30-04-2003 10:48PM

Yes, but if you can even conceive initially a circle with infinite radius on the plane, then how can you possibly work with conventional euclidian geometry to counter SOL's little supposition?

ecksor · 30-04-2003 10:57PM

Originally posted by Sev
Yes, but if you can even conceive initially a circle with infinite radius on the plane, then how can you possibly work with conventional euclidian geometry to counter SOL's little supposition?

Is that the first time that anyone has mentioned a specific geometry on this thread? The first post I made on this thread was to try and establish where exactly all this stuff was supposed to be going on. (I tend to think of circles on the plane of R2).

Anyway ....

Parallel lines not meeting doesn't imply euclidean geometry. Check out Gauss's work on trying to disprove the parallel postulate, where he showed that it was a necessary axiom in euclidian geometry, and that parallel lines in one geometry can look quite different to parallel lines in another geometry.

ecksor · 30-04-2003 11:20PM

Originally posted by ecksor
Check out Gauss's work on trying to disprove the parallel postulate

Heh. Of course, he didn't try to disprove it, he tried to show that it was unnecessary in euclidean geometry.

SOL · 30-04-2003 11:32PM

So in conclusion a line is a circle of infinite diameter and this makes maths out by an infinitly small ammount but due to the nature of infinity the harder you look the straighter the line is, so we are argueing about what now?

ecksor · 30-04-2003 11:40PM

Originally posted by SOL
So in conclusion a line is a circle of infinite diameter

You haven't proved this. [edit]or told us what system of geometry the two are supposed to be equivilent in[/edit]

Are you studying geography or geology by any chance?

bonkey · 01-05-2003 09:19AM

Originally posted by Sol

So in conclusion a line is a circle of infinite diameter and this makes maths out by an infinitly small ammount

In conclusion???? Sol, you havent put forward a single argument strong enough to draw a conclusion from, and you sure as hell havent gotten concensus.

You have utterly failed to show that a finite-length line is an arc of a circle of infinite diameter, and instead are just insisting that its true....which is really what you've been doing from the start. Whats wrong, did I scare you when I asked for the proof of your assertion? How can you offer a conclusion without your prood?

At the very simplest level, you are assuming that the curvature of a circle with infinite radius is 0. This is fundamentally incorrect. It is an infinitely small non-zero value.

1/infinity <> 0

This is the infinitely small amount that you are out by...not mathematics.

Although at this stage, I think you either dont know mathematics well enough to be able to succintly argue your point, or you do know mathematics well enough and are deliberately trolling.

In either case.....my conclusion is that I have better things to do with my time then continue to answer your posts until you actually offer a solid argument rather than an empty assertion.

jc

Victor · 01-05-2003 01:36PM

Isn't this like the divided by zero / divided by infinity argument? Teh circumfereance of a circle of infinite diameter will tend towards straight, but not actually be straight, i.e. all arcs tend towards being straight (depending on scale).

But to take the correlation that all straight lines are actually arcs is wrong.

Kantankerous · 02-05-2003 09:40AM

...to take the correlation that all straight lines are actually arcs is wrong.

Amen to that.

Victor · 02-05-2003 08:53PM

Originally posted by Victor
But to take the correlation that all straight lines are actually arcs is wrong.

Actually if you accept by the nature of infinity, that there are an infinite number of lines and indeed an infinite number of straight lines and alledgely some of those "straight" lines might be arcs, there must still be some of those "Straight" lines that are not arcs.

:rolleyes:

CuLT · 03-05-2003 12:47AM

quodlibertarian -
A pedantic person who engages in elaborate arguments about minor things

Nuff said, this is an arguement that can't be solved on boards...

Line is a Circle

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