1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Colourful space
  1. Metric Spaces (Replies: 26)

  2. Plane in the space (Replies: 1)

  3. Lorentz space (Replies: 0)

  4. Normed space (Replies: 5)

Loading...