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# Expected Distance

### #1

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?

### #2

Posted 06 May 2014 - 11:34 PM Best Answer

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

- Bertrand Russell

### #3

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

### #4

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...

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

- Bertrand Russell

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