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Do parellel lines ever meet?

Pzyko

The point is that a line that follows a non-flat plane isn't straight other than with respect to the plane.

Or with respect to a surface that's parallel to the plane (and there are an infinite number of such surfaces). Flatness is relative anyway...

Reply 41

Pzyko_1827

Squishy

Or with respect to a surface that's parallel to the plane (and there are an infinite number of such surfaces). Flatness is relative anyway...

And now we see why it's a stupid concept.

Reply 42

Squishy

11

Pzyko

And now we see why it's a stupid concept.

Why do we see that now? Spherical triangles exist everywhere in the real world. It's not just a concept.

Reply 43

Pzyko_1827

Squishy

Why do we see that now? Spherical triangles exist everywhere in the real world. It's not just a concept.

Lol. I'd like to put an end to this. In conclusion, the chemistry teacher only thought that the concepts of maths and physics were stupid because his understanding was incomplete :smile:

.

Reply 44

Squishy

11

Pzyko

Lol. I'd like to put an end to this. In conclusion, the chemistry teacher only thought that the concepts of maths and physics were stupid because his understanding was incomplete :smile:

.

Well, all of our knowledge is incomplete. :smile:

I'll be the first to admit I think quantum physics is stupid because I don't understand it...stupid cat that's alive and dead at the same time.

Reply 45

shiny

12

Pzyko

Lol. I'd like to put an end to this. In conclusion, the chemistry teacher only thought that the concepts of maths and physics were stupid because his understanding was incomplete :smile:

They're not necessarily stupid but there isn't necessarily much practical use (that matters to us in day to day life) for a lot of the work that has been done in mathematics and physics.

Reply 46

Pzyko_1827

shiny

They're not necessarily stupid but there isn't necessarily much practical use (that matters to us in day to day life) for a lot of the work that has been done in mathematics and physics.

I think the use of the phrase "loads of bollocks" implies stupid.

hear hear

elpaw

parallel lines meet at infinity. since infinty is "never", no, parallel lines do not ever meet, unless they are the same colinear.

so can I say they converge at infinity?
If so, I ve got a problem:
Consider on a Catesian plane the lines y = 0 and y = 1
They are parallel and do not coincide
If parallel lines meet at infinity, the lines y = 0 and y = 1 converge at infinity
and then
limit(x->infinity)0 = 1 and limit(x->infinity)1 = 0?? :confused:

Reply 49

fishpaste

keisiuho

so can I say they converge at infinity?
If so, I ve got a problem:
Consider on a Catesian plane the lines y = 0 and y = 1
They are parallel and do not coincide
If parallel lines meet at infinity, the lines y = 0 and y = 1 converge at infinity
and then
limit(x->infinity)0 = 1 and limit(x->infinity)1 = 0?? :confused:

Converge? I don't think that lines can converge, because the ones you mentioned have zero gradients. But lines can intersect, so say that y = 0x and y = x^0 are parallel lines, it's probably not very rigorous, but you could say that they intersect when

0x = x^0
divide both sides by x

0 = x^-1 = 1/x
x = 1/0 or infinity.

Reply 50

shiny

12

fishpaste

Can you take a limit of something to infinity like that? Would it not be more correct to say limit(x->infinity) 0x = 1

Yep

Reply 51

fishpaste

shiny

Yep

Yep to which bit?=P

Reply 52

Squishy

11

Maths tends to fall apart at infinity. I prefer to stay with the good old finite numbers.

Reply 53

shiny

12

fishpaste

Yep to which bit?=P

lim (x->infinity) 1 = 0 (i.e. where's the x?)

Reply 54

Jamie Frost

OP

6

Squishy

Maths tends to fall apart at infinity. I prefer to stay with the good old finite numbers.

Actually I'm inclined to agree considering we live in an infinite universe :smile:

Both infinity and 0 are always a problem in maths, you can use it to prove 1=2 and all sorts of bizaare stuff.
And btw, when I said two lines having a gradient of 1, I meant one with gradient 1 and one with -1, I just assumed some symmetry in the situation.

I'm glad to see this topic has gone back on-topic after turning into a boring debate on what a triangle is. :tongue:

Reply 55

RobbieC

15

At infinity there will be an instantaneous crossing of the parallel lines, or so they are called :biggrin:

. However, I think it is wrong to say they would converge, unless they are lamina, in which case there is an extra dimension to consider. For someone who is not very clever; that sounded particularly mathematical.

Questions for Squishy:
How old are you (personal, sorry, but I am curious...)?
Where do you come from (again, optional due to its personal nature)?
How on Earth did you become so intelligent? Most of the time I can understand the more intelligent members on this forum, MOST of the time. However, everytime you open your proverbial mouth, its like hearing God speak...

Sorry for the questions. You are just someone who caught my eye, and I fancied finding out about!

Reply 56

Squishy

11

RobbieC

Questions for Squishy:
How old are you (personal, sorry, but I am curious...)?
Where do you come from (again, optional due to its personal nature)?
How on Earth did you become so intelligent? Most of the time I can understand the more intelligent members on this forum, MOST of the time. However, everytime you open your proverbial mouth, its like hearing God speak...

Sorry for the questions. You are just someone who caught my eye, and I fancied finding out about!

Err...I really don't know what you mean about my intelligence...there are lots of very smart people here. :smile:

But I'm 18...just finished my A-levels a few weeks ago. Hopefully off to university in October. I was born in China, but I've lived in England most of my life. How about yourself? Are you going into the Upper 6th next year?

By the way, since you live in Chelmsford, do you mind telling me if you've ever seen this roadsign? A friend emailed it to me saying it was real, but I think she was taking the piss.

different geometries are based on three possible states for parallel lines :
never meeting (flat or Euclidean)
must cross (spherical)
always divergent (hyperbolic)
or one can think of triangles where for a flat Universe the angles of a triangle sum to 180 degrees, in a closed Universe the sum must be greater than 180, in an open Universe the sum must be less than 180.
although it is possible to add to the real plane a "line of infinity" see http://encyclopedia.thefreedictionary.com/Line%20at%20infinity and so parallel lines can meet with this closure of the plane added.

Reply 58

RobbieC

15

Squishy

Err...I really don't know what you mean about my intelligence...there are lots of very smart people here. :smile:

But I'm 18...just finished my A-levels a few weeks ago. Hopefully off to university in October. I was born in China, but I've lived in England most of my life. How about yourself? Are you going into the Upper 6th next year?

By the way, since you live in Chelmsford, do you mind telling me if you've ever seen this roadsign? A friend emailed it to me saying it was real, but I think she was taking the piss.

No kidding. It really does exist. However, the bunker has not been in use for years now, and so it doesn't need to be a secret anymore!

As for your counter-enquiry...

I am 17, and will be 18 come September 1st :biggrin: