Yes, very elegant, concise and elementary. Indeed, very nice!

@Lior--thanks for the reference; I was hoping to learn more about this problem.

@Gil Kalai: Well, now that you've edited it, it seems fine to me. Some may say there is not enough "motivation" but some questions are self-motivating, i.e. they don't require lots of explanation. This one seems to me to be in that category

The problem with re-writing a better but thematically similar question is that everybody here has an answer, but the question has been taken away! How to turn an answer into a question, that's my problem!

Furthermore, it is true that the original post had severe grammatical errors. Nevertheless, in essence the question remains as first stated. Like many simple questions in mathematics, it opens the way to some much deeper ideas.

BTW, has anyone heard from AJAY, our OP? He doesn't seem to have stuck around for the discussion!

Quite frankly I fail to see what's "unreal" about this question.

Finally (again), I wiki'ed "curvature" when I wrote my previous comment, and at least in that article I didn't see the whole stuck as hinted at here, though I didn't review the entry thoroughly--this time. "There's more things in heavan and earth, Horatio, than you'll ever find in your wiki article."--Bill Jerkspeare.

@sleepless--I by no means fell we're at odds on this subject. I tried to write with severe brevity since I'm working in "comment space", not "answer space". (BTW, can closed questions be answered? I was under the impression the answer is "no".) Anyway, being cognizant of the geometric sense in using "per length" than "per parameter increment" I mentioned a more differential geometric approach, which I believe clarifies the issues.

More, to beat the 500 character limit: Finally, I think a more geometric view of physics (say a la Einstein) sees space and time on a more equal footing. Nath'less (as Chaucer would say), I basically agree with sleepless. We're in the same chapter, if not on the same page. Again, there's more here than meets the eye, as Dick and sleepless have noticed.

Though I basically agree with sleepless, please note that in my comment I said that $d^{3}y/dx^{3}$ is related to curvature, not that it is curvature! Also, the outworking of these ideas in a coordinate-free differential geometric notation will give (I betcha!) rate of change of curvature with arc length (the natural parameter for a curve; then the tangent vector is of unit length).

If I could vote on such matters, I would vote to re-open as well.

Since the second derivative basically relates to curvature, viz. for a simple "curve" $y = f(x)$ we have $k = (d^{2}y/dx^{2})/(1 + (dy/dx)^{2})^{3/2}$, the third derivative relates to the rate of change of curvature. This could seemingly be worked out in coordinate-independent terms using tangent and normal vectors, etc. (Think Frenet-Serre formulae.) My guess is that, in $R^{3}$ and higher (dimensions), torsion etc. enters in. So it seems there is some geometry here after all!

Whatever happened to old James? I was hoping he'd respond with a little more information about the stage of his mathematical development.

And so we'd best not judge--either way--at all.

I may be mistaken, but perhaps you mean Neumann boundary conditions, I believe a different guy from von Neumann.

BTW, it's not entirely clear to me the OP is in university, although his reference to "more advanced" courses indicates some exposure to college-level curricula.