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Math Help - Square metric

  1. #1
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    Square metric

    The square metric defines the distance between two points (x1, y1) and (x2, y2) in R^2 by:

    D((x1,y1),(x2,y2)) = max{|x2 - x1|, |y2-y1|} where the function max{a,b} denotes the larger of the two real numbers a and b.

    Sketch all points (x,y) in R^2 such that D((0,0),(x,y)) = 1. Measure angles in the usual way. Show by example that R^2 with the square metric does not satisfy the SAS Postulate.


    I've already graphed the points that satisfy D((0,0),(x,y))=1. It is the square formed by connecting (1,1), (1,-1), (-1,1), (-1,-1). However, I'm not sure what they mean by using the square metric to show it does not satisfy SAS. Help please!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by spectralsea View Post
    The square metric defines the distance between two points (x1, y1) and (x2, y2) in R^2 by:

    D((x1,y1),(x2,y2)) = max{|x2 - x1|, |y2-y1|} where the function max{a,b} denotes the larger of the two real numbers a and b.

    Sketch all points (x,y) in R^2 such that D((0,0),(x,y)) = 1. Measure angles in the usual way. Show by example that R^2 with the square metric does not satisfy the SAS Postulate.


    I've already graphed the points that satisfy D((0,0),(x,y))=1. It is the square formed by connecting (1,1), (1,-1), (-1,1), (-1,-1). However, I'm not sure what they mean by using the square metric to show it does not satisfy SAS. Help please!
    Hmm...Side Angle Side? haha
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  3. #3
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    I know what SAS means. I can't figure out how they want to disprove it by means of this square metric.
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by spectralsea View Post
    I know what SAS means. I can't figure out how they want to disprove it by means of this square metric.
    Well, I don't know what the SAS postulate is. What is it?
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  5. #5
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    "If triangle ABC and triangle DEF are two triangles such that AB=DE, <ABC=<DEF, and BC=EF, then triangles ABC and DEF are congruent"

    *edit* Nevermind, I solved the issue. I was interpreting the wording of the question incorrectly.
    Last edited by spectralsea; January 31st 2010 at 06:17 PM.
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  6. #6
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    Re: Square metric

    I am new to this topic. Where can I find more information about square metric, and in particular, how it relates to parabolas, ellipses, hyperbolas and circles
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