Can you calculate Pi using a Solver?

[EdS2]

(12-12-2019 05:49 PM)Valentin Albillo Wrote:  

(12-12-2019 03:02 PM)EdS2 Wrote:  Merely evaluating an expression doesn't feel like it's making proper use of a solver.)

Frankly, I don't understand why you're so fixed in solving something (as in finding the root of some equation, say) and think evaluating expressions isn't "proper use of a solver".

It's a good question, and I haven't managed to be clear, for which I apologise. I wonder if I can do better...

For me, this challenge, like many, is about constrained programming of a kind. If I had a programmable calculator, I might want a challenge which was to write a program. If it was not programmable, but had an Integrate command, I might want an interesting challenge which involved integration. But if it was programmable, I might still be interested in a challenge to use the Integrate command in an interesting way. Or indeed, I might be interested in a challenge to write a program for numerical integration, which doesn't use the Integrate command.

So it is with this challenge. I'm thinking of a solver as a complex feature which finds roots to an equation - preferably not an easy equation like x^2-3=0 or 1/x-4=0 but an equation which we couldn't readily solve ourselves, like x^4+x^5-e^6=0. But I want the root found to be pi, not a specific number that's close to pi but not equal to pi. And I think, as yet, I haven't seen such an equation - maybe there isn't one.

(Of course, an equation like sin(x)=0 could suffice, but it's trivial, which is why I wanted to avoid use of trig functions.)

It's always interesting to see various ways to compute pi: sums, products, nested surds, iterative algorithms, even spigots. And this, I'd hoped, is another possible way.

Hope this makes things a bit clearer. (And I'm still glad to see all the various contributions and references!)