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Colourful space

  1. Mar 7, 2007 #1
    Hi everybody, I am unable to tackle this problem, and don't know how to attack it. can someone plz help me how to attack the following problem.

    Q. Suppose colour every point in 3-D space is assigned one of the three colours- red,green,blue.Can i conclude the following???:

    1)there must exist a right triangle which has three of the vertices of same colour.

    2)there must exist an equilateral triangle which has all its vertices of same colour.

    3)the problems 1 and 2 with the additional fact that there exist infinitely many such in any region of space.

    4)there must exist a monochromatic line.

    5)there must exist a monochromatic circle.

    plz give some hints.
    thank you.
    Jitendra
     
  2. jcsd
  3. Mar 8, 2007 #2

    cristo

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    Show some work! What do you think?
     
  4. Mar 8, 2007 #3
    I don't know how to approach it...but know that it is based on the concept of denumerability of real numbers. I don't want complete help but just few hints so that i can do it myself.plz help.

    thanks
     
  5. Mar 8, 2007 #4
    The real numbers aren't denumerable though. That is they are not countable, or there exists no bijection between the reals and the natural numbers.
     
  6. Mar 9, 2007 #5

    StatusX

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    Homework Helper

    I don't think there are any advanced math tricks that'll help you. You just need to think it through for a while. To get you started, the first one is true if the space is 2D. Can you prove this?
     
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