[VA] SRC#005- April, 1st Mean Minichallenge

[Valentin Albillo]

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Hi, Mike:

(04-15-2019 09:29 PM)Mike (Austria) Wrote:  Thanks Valentin for this inspiring minichallenge. I particularly enjoy math riddles when they involve little-known facts about well-known mathematics. This one definitely fits this description particularly well - the fact that the various means are discrete members of a continuous family had escaped my attention so far (for decades - embarrassingly enough :-) ).

You're welcome, thanks to you for your interest and awesome posts on this minichallenge. And I agree with you, I'm also enthralled when I find an interesting piece of mathematics that happens to be new to me, so my goal has always been to post the kind of articles and challenges that I myself would like to read and solve.

Quote:Since there have been no solutions for RPL, let me share my take on this. It should work for any version of RPL starting with the HP48G(X).

Great ! I always welcome RPL solutions, they tend to be a little on the cryptic side but yours qualifies as an exception, pretty clear code made even clearer by your generous assortment of comments.

Quote:I like the terseness of this function.

Terse it is, and the results are of course correct.

Quote:A further step in generalizing the mean is by replacing the \(p\)-th power of \(x_i\) by applying an arbitrary continuous strictly monotonic function and taking its inverse after computing the sum and dividing by \(n\).

Yes, it's an interesting way of generalizing it further. Nice addition to the subject matter.

Quote:Why pick one of the original list elements to estimate the solution: we make no assumptions about the domain of \(f\). [...] This is cheaper than e.g. taking the arithmetic mean as an estimate or bracketing the solution by searching the minimum and maximum of {\(x_i\)}.

Cheaper or not, I would've used the minimum/maximum as they're immediately available without search using the available matrix functions and they certainly bracket the solution perfectly. Not to say that your method isn't perfectly adequate, of course.

Quote:I hope all this makes sense. Setting up these functions was fun - thanks for giving me an excuse to learn and play with stuff i'd otherwise never have looked at again. Despite RPL's deficiencies (such as handling many trivial cases incorrectly), I like the expressive power and abstraction / object orientation of this language.

I'm glad you enjoyed it all and thanks again for your extensive, very interesting post (from which I also learned interesting things) and for your time, much appreciated. Oh, and welcome to the new forum, for a very first post you did really great ! ...

Best regards.
V.
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