I am reading papers at the moment that describe an analysis of overhead of a system and as part of the analysis they estimate the distance between two random points in a square.
The first paper Iím reading says the distance between two random points in a square is sqrt(2)/3. They didnít say where they got this from but I found a reference listed here:
http://answers.yahoo.com/question/index?qid=20081027054058AAPMIWO Mr F says: Wrong.
The second paper Iím reading also needs the distance between two random points in a square and state that the formula used in paper 1 is used incorrectly (they donít say why). They suggest using the formula which would give a value of 0.521405433 (1/15[sqrt(2) + 2+ 5ln(1+sqrt(2))])....sorry for the notation.
I found a reference for that here:
http://mathworld.wolfram.com/SquareLinePicking.html Mr F says: Correct.
Then I read a third paper and they stated that the average geometrical distance between any two random points in a square of side length L is 2L/3. Mr F says: Wrong. It probably meant to say that the SQUARE of the average geometrical distance is 2L^2/3.
Can someone please explain to me which equation is correct and/or why variations might exist (and also if one of these is simply out and out wrong).
Thanks in advance.