/sci/ - Science & Math

The second statement is indeed the logical converse of the first, but the converse of a true statement is not necessarily true.

>>5746519
Right, that's why I'm asking. Sometimes the converse is true in geometry and sometimes it isn't, in this case I'm trying to think of a counter example and I can't think of any.

>>5746523

In that particular case it's true, yes. (Assuming Euclidean geometry.) But it seems redundant - by what method are you determining that they are everywhere equidistant that doesn't already prove they're parallel?

>>5746531
Well it's for a regular octagon, I'm trying to show that a diagonal is parallel to one of the sides, forming an isosceles trapezoid. In this case, I know nothing of octagons in terms of properties they have. So I'm trying to break it into bits of what I do know, such as quadrilaterals and triangles. It's not really important, it's more for myself than for the class.

>>5746516

Yes

\thread

>>5746545
Ok, thanks.

>>5746516
No.

Consider the line containing all points (x, 0, 0).

Consider the line containing all points (0, y, 1).

Equidistant. Not parallel.

>>5746545
>dat filename

>>5746516

A circle with diameter 4 and a circle with diameter 2 and the same central point will be equidistant all around, but the lines would not be parallel. Work with spirals as well

>>5746572
Do you know the difference between a line and a curve?
No, you don't.

>>5746565
>Equidistant.

How do you figure?

Can the lines be mirrored curves?

>>5746575
Curves aren't a type of line?

Didn't know the thread was still up. We're working with just a simple plane here, here's the problem I was working on. I'm still writing out my argument for the answer I got (which ended up being 24(2)^(1/2)+24), but I'm feeling confident with the argument I've developed.

>>5746565

>worth restating

In Euclidean Geometry, two parallel lines (in a plane) are indeed everywhere equidistant.

In Hyperbolic Geometry, two lines can be parallel, but be further apart some places than others.

The proof of this quiet easy and truly marvellous. I do not have the time or room to type it in this small box.

>>5746572
But the tangent lines would be parallel for any given point on the two circles, no?

>>5746586

Curves are lines what is that guy talking about.

Curves follow a line they just arent STRAIGHT lines.

>>5746575

Hey genius, plot the line: y = x^2

>>5746675
That's not a line.

>>5746626
Not the way you're wording what you mean. Any two tangential lines will not always be parallel for two points on the circle unless they're tangest at pi rad apart.