@Markiyan Hirnyk 

Apparently,

"The expected value of the distance between two random points in a box was stated as
 a problem by D.P. Robbins, [5], and calculated by T.S. Bolin, [3]."

....
[3] T.S. Bolis Solution of problem E2629: Average Distance between Two Points in a Box, 
Amer. Math. Monthly Vol. 85, No. 4. pp. 277-78, April. 1978.
...
[5] D.P. Robbins Problem E2629: Find the Average Distance between Two Points in a Box, 
Amer. Math. Monthly [1977,57].
............
The same method was also used here:
http://www.math.utep.edu/Faculty/moschopoulos/Publications/1999-Distance_Between_Random_Points_in_a_Cube.pdf
As for higher dimensions, the same author (Johan Philip, as I posted initially) provides this
http://www.math.kth.se/~johanph/h45.pdf
Note:"The obtained expressions contain unsolvable integrals"

 Edit: formatting issues

Please can you post your code here.

I have to take issue with your view that factoring quadratics is unimportant or overemphasized. Personally I think it's a fundamental skill that transfers well to, and aids in, other more advanced techniques in applied maths. The mental juggling you mention is a quite important skill if a student is to continue their study in maths. That said, your applet looks very useful for helping those students who might be struggling with it.

Perhaps one of the reasons students find difficulty with factoring is due to the point at which factoring is taught. In my view, there is a lot to be said for this sequence:

1. Parabolas in the real world;
2. Graphing quadratics;
3. Visually finding zeros;
4. Factoring, with the connection to zeros hopefully coming out easily;
5. The quadratic formula;
6. Completing the square, with (depending on the aptitude of the students) the derivation of the quadratic formula.

Speaking for myself, I didn't come across the factor-remainder theorem (formally, that is) until I was at university, while I learned quadratic factorisaton at around 14 yrs old. It's probably safe to say that I was "bludgeoned" with it, but it definitely didn't do me any harm....

Hi Christopher

The laptop has been great so far (fingers crossed).  I did have a little issue with it  completely freezing up spontaneously, soon after purchase, but Sony support people were very good and new device driver fixed it.

Yes, I have Maple 15, and I am interested in parallel processing, though unfortunately I don't have the time to look into it much. I will be doing a lot of statistical computing in a few months so I hope to investigate a bit before then

@pagan  I think those are good suggestions, pagan. It is certainly a problem that the seemingly majority of questions are posted by new users, and so the answerer will not get up-voted by the questioner. Personally, when I see a good answer to a newbie question, I always upvote it.

@Christopher2222 It seems obvious to me that some people will have different reasons for partipating on mapleprimes than others. Personally, I am here to learn, but if I can help others and get up-voted along the way that's nice but it's not my main reason. For experts such as Alec and a few others, I doubt there is much they can learn here, so why shouldn't they get the small reward of a ittle ego-stroking ?

@Alec Mihailovs I would like to know why/how adiban has 1000 points and 11 badges for (apparently) doing nothing. 

@pagan  I think those are good suggestions, pagan. It is certainly a problem that the seemingly majority of questions are posted by new users, and so the answerer will not get up-voted by the questioner. Personally, when I see a good answer to a newbie question, I always upvote it.

@Christopher2222 It seems obvious to me that some people will have different reasons for partipating on mapleprimes than others. Personally, I am here to learn, but if I can help others and get up-voted along the way that's nice but it's not my main reason. For experts such as Alec and a few others, I doubt there is much they can learn here, so why shouldn't they get the small reward of a ittle ego-stroking ?

@Alec Mihailovs I would like to know why/how adiban has 1000 points and 11 badges for (apparently) doing nothing. 

@Alec Mihailovs , of course it is only temporary. You have to take for granted that there will be some spam if you operate a public forum and consequently some overhead in managing it. Deleting an account is a perfectly reasonable response to accounts that are being persistantly abused

I think that's great, Alec.

@Alec Mihailovs 

I agree that a piecewise interpolation may give a better idea of what is happening with the data, but if the purpose of the exercise is to perform interpolation on points in between, then depending on the application, smoothness might be essential while the plot posted by Christopher in the OP shows that for Maple's piecewise polynomial spline does not suffice.  I came accross Catmull-Rom splines as a special case of a cubic Hermite spline (following the wiki link you gave above), and I found some useful information here:

http://www.cs.cmu.edu/~462/projects/assn2/assn2/catmullRom.pdf

@Alec Mihailovs 

I agree that a piecewise interpolation may give a better idea of what is happening with the data, but if the purpose of the exercise is to perform interpolation on points in between, then depending on the application, smoothness might be essential while the plot posted by Christopher in the OP shows that for Maple's piecewise polynomial spline does not suffice.  I came accross Catmull-Rom splines as a special case of a cubic Hermite spline (following the wiki link you gave above), and I found some useful information here:

http://www.cs.cmu.edu/~462/projects/assn2/assn2/catmullRom.pdf

Alec, is it possible to use that method while maintainng smothness ?

Alec, is it possible to use that method while maintainng smothness ?

@Christopher2222 I don't know why someone would downthumb you, but I think you need to be more speciic about what you mean by "exact fit". Based on your annotated plot, it looks like you want to reduce the maxima and increase the minima. Maybe another way to think of it would be to fit piecewise polynomials with undetermined coefficients, and minimise the distance between the points (calculus of variations), while maintaining the requirement that the first derivatives are equal on each side of the points..... ?

He's at it again ! Why can't the account be disabled, deleted, or whatever ? Is it only I who is irritated by this nonesense ?

What do you mean by "exact" ?