related to geometry

Discussion in 'Homework Help' started by Ak_47, Feb 15, 2011.

  1. Ak_47

    Thread Starter New Member

    Dec 19, 2010
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    this one is about linear algebra..
    defintion of dimension says that dimension of an object is the minimum no of coordinates needed to secify each point within it....and line is single dimensional....... we also know that in order to specify a point on line we minimum need two coordinates(x,y) how can we justify line has just oone dimension?????? i am bit confused...... hope some one can point out where am i wrong????
     
  2. magnet18

    Senior Member

    Dec 22, 2010
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    it is a one dimensional object in a two dimensional plane, if that makes any sense. You need to locate its start and end points in both the x and y directions.
    if you had a one dimensional "world" (a line) you could specify a point with only one coordinate.
     
    Last edited: Feb 15, 2011
  3. Ak_47

    Thread Starter New Member

    Dec 19, 2010
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    do u mean that in real life line behaves like a two dimensional object.........
     
  4. magnet18

    Senior Member

    Dec 22, 2010
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    Nope, a line is a one dimensional object, always.
    No matter what angle you view it from it only has length.
    It has two dimensions on an (X,Y) graph because its endpoints are not constrained to one dimension; it's a one dimensional object in a two dimensional graph, if that makes sense.
    There is only a one dimensional line between any two points.
     
    Last edited: Feb 15, 2011
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  5. Georacer

    Moderator

    Nov 25, 2009
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    In order to specify a point in a line, you need only one dimension; only one number can describe the point exactly.

    Think about a ruler. To describe a tickmark on a ruler you only need one number: its magnitude.

    Maybe what you are confused about, is that when you define a line on a 2D plane, you use two numbers x and y to describe a line on it: y=ax+b. But this time, you work in the domain of the 2 dimensions and (x,y) might as well describe any point on the plane. The extra equation actually reduces the 2 degrees of freedom to only 1. Then you come back to the 1-dimensional system.

    The line can still describe its points, say through the quantity "t". But in the plane, the same points need to be describe with two quantities (t , a*t+b).
     
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