All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Mean Distance Two Points (Posted on 2013-06-01) Difficulty: 3 of 5
[1] What is the mean distance between two random points on the perimeter of a unit square?

[2] What is the mean distance between two random points on the interior of a unit square?

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Part 2 in two different ways. | Comment 2 of 8 |
First way:  I began by finding the mean distance between two points on a unit segment by what is basically a double integral.  I do not doubt the result I got:  1/3.
Next I made an assumption that I don't know is valid:  I simply found the distance between two points whose x and y coordinated each differ by 1/3:  √(2)/3 ≈ .4714

This does not agree with Charlie's finding so I doubted it and decided to try a different method.

Second way:
I broke the unit square into n congruent squares and considered the center point of each small square.  For n=2, 3 & 4 I calculated the distance between each of the (n) possible selections of two of these points.  The mean distances are as follows.
(8+4√2)/32 ≈ .4268
(48+24√2+16√5)/243 ≈ .4844
(136+80√2+48√5+24√10+16√13)/1024 ≈ .4785
This may be taken as evidence supporting my first solution  (as opposed to Charlie's.)  It may also be that both of my methods suffer a similar error.

Anyone care to write a program to increase n?  I can flesh out the details is needed.

  Posted by Jer on 2013-06-02 01:10:39
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information