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Expected Distance


Best Answer bonanova, 06 May 2014 - 11:34 PM

Spoiler for Depends

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#1 BMAD

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Posted 06 May 2014 - 02:01 PM

What is the expected distance of two points in a unit square?

 

What is the expected distance of two points in a regular unit pentagon?

 

Does the expected distance between two points in a regular unit n-gon converge as n goes to infinity?


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#2 bonanova

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Posted 06 May 2014 - 11:34 PM   Best Answer

Spoiler for Depends


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 m00li

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Posted 07 May 2014 - 12:31 AM

Spoiler for Depends

how do we find the mean distance for a square? and for a regular unit pentagon? seems very very tough to me :(


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#4 bonanova

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Posted 07 May 2014 - 12:41 PM

Empirically, by simulation. Or do some area integrals.

 

For an equilateral triangle with unit sides it's 0.364791843300... 
For a square with unit side it's 0.521405433....
For a circle with unit radius it's 0.905414787...


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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