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    (Original post by 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...
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    (Original post by 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.
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    (Original post by 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.
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    (Original post by 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 .
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    (Original post by 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 .
    Well, all of our knowledge is incomplete. 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.
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    (Original post by 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
    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.
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    (Original post by 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 *******s" implies stupid.
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    hear hear
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    (Original post by 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:
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    (Original post by 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.
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    (Original post by 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
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    (Original post by shiny)
    Yep
    Yep to which bit?=P
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    Maths tends to fall apart at infinity. I prefer to stay with the good old finite numbers.
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    (Original post by fishpaste)
    Yep to which bit?=P
    lim (x->infinity) 1 = 0 (i.e. where's the x?)
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    (Original post by 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
    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.
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    At infinity there will be an instantaneous crossing of the parallel lines, or so they are called. 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!
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    (Original post by 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. 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.
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    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.thefreedictionar...0at%20infinity and so parallel lines can meet with this closure of the plane added.
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    (Original post by Squishy)
    Err...I really don't know what you mean about my intelligence...there are lots of very smart people here. 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. Date books everybody!
    I am in the lower sixth, and have just finished my AS levels... but I think ive fluffed up my maths exams

    What A levels did you do Squishy? And where have you applied for offers (which did you get?) etc...
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    (Original post by visesh)
    gud point. but seeing as this is a maths forum...
    yes,at infinity.
 
 
 
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