## Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

# 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

*Vidi vici veni.*

### #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...

*Vidi vici veni.*

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users