Colourful space

  • #1

Main Question or Discussion Point

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
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,107
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Show some work! What do you think?
 
  • #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
 
  • #4
1,074
1
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
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.
 
  • #5
StatusX
Homework Helper
2,564
1
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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