Recent content by FranzS

I was there a few months ago.

Thanks for the insights. I'm going to learn something new.

In order to interpolate a number ##m## of points ##(x_i,y_i)## with a polynomial ##P_n(x)## of grade ##n = m-1## (assuming all ##x_i## have different values), one has to solve the linear system... $$ \begin{flalign*} & y_i = \sum_{k=0}^n \beta_k \, {x_i}^k \quad \quad \forall \, i=1,2,...,m &...

I've checked and I think I had Indeed written something wrong into Desmos, the equations are correct. Again, thank you @andrewkirk for you super valuable review

Dear @andrewkirk , thanks a lot. I'll double check everything later.

First of all, thank you so much @andrewkirk for taking your time to study this "obsession" of mine. I'd like to update this thread with some further research I've done lately, in case anyone is curious about it. I'm analyzing a simpler case, for which I can get a correct solution when ##M=2##...

Nice intuition!

Nice to know! I'll try that.

Also, choose the sampling points wisely (i.e. denser where your shape is steeper).

Yep, this can always be done by hand, but the calculations (i.e. solving the linear system of ##n## equations) get exponentially more time consuming. I did that with ##n=2## (quadratic fit) and it took me four to five pages of writing. The drop-like shape will probably require a quartic...

Hello, I'm facing a practical optimization problem for which I don't know whether a standard approach exists or not. I would have liked to rephrase the problem in a more general way, for the sake of "good math", but I'm afraid I would leave out some details that might be relevant. So, I'm going...

If the "piston" is not sealed, as you said in your first post, the pressure is the same within the whole enclosure. The "piston" therefore is not really a piston, but a retaining flange of the rod, as someone correctly pointed out. The force exerted is then equal to the fluid pressure times the...

In case of an integral ##\rightarrow## differential equation of the type: $$ f(t) = \int_0^t g(f(\tau)) d\tau $$ $$ \rightarrow \frac{df(t)}{dt} = g(f(t)) $$ which turns out not to be solvable in exact form because ##g(f(t))## is a non-polynomial function (but it would if ##g(f(t))## was a...

Is this some math exercise or do you want it to be of any actual use for tennis practice? Drag and Magnus effect due to ball spin are not negligible in the real world.

Loosely speaking... Vacuum is just the absence of air, and it does not "pull". It is really air that "pushes". You don't see the effects of the relatively high "pushing force" of the atmospheric air because for the most part it is counter-balanced (for instance, fluids inside the human body are...