[python/square-root] Add mentoring doc

[antoniouaa]

Hello, my attempt at mentoring notes for square-root for python.
I see there's already been a past attempt at introducing this mentoring document , in #2251.

Document includes sections suggesting and explaining 2 different solutions, main solution using Heron's method from the wiki pages linked in the description of the problem.
I understand that's what the problem statement is pushing people to investigate and implement, instead of using cheap hacks like ** 0.5 and pow.

Comments welcome!

[IsaacG]

Why would sum not be allowed?

[antoniouaa]

I'm not sure exactly why, but it's mentioned in the exercise instructions as an example builtin to avoid.

Python offers a wealth of mathematical functions in the form of the math module and built-ins such as pow() and sum(). However, we'd like you to consider the challenge of solving this exercise without those built-ins or modules.

I can see at least 2 commmunity solutions where this function is used, inappropriately I might say:

1. https://exercism.org/tracks/python/exercises/square-root/solutions/PetaGb
2. https://exercism.org/tracks/python/exercises/square-root/solutions/soroushmz

[BethanyG]

That instruction append is a nudge, as opposed to "absolutely not allowed". We're trying to (gently) discourage the x**.5 sort of solution (or at least prompt the student to do some hard thinking about it). However, if a student really doesn't want to do that -- it's their choice.

So maybe the mentor notes should have an example of how you'd use sum() in an appropriate way, or maybe some discussion points on how to move a student from the x**.5 solution toward a sort of intermediate solution, and eventually to the full Heron's.

What is the benefit of solving this problem "the long way around"? What could a student learn/get better at if they took on the challenge?

[antoniouaa]

Mentoring notes can't really force a student to change their solution and I don't think the first couple lines suggest it absolutely shouldn't be done using **. Students could even hardcode values to fool the tests.

I imagine that people who asked for mentorship did so for 2 reasons:

1. Their solution is too simple and are wondering if there's more to it,
2. They tried implementing one of the methods in the wiki articles and want to improve on that implementation.

The spirit of the exercise is not to use a builtin operator, but to investigate other methods of doing the calculation without it.

Heron's method happens to be the simplest, its the first method linked in the wiki page, there's no intermediate step between ** or math.pow and that.

It's Heron's method that's the intermediary step, Newton's method and binary search (included as an alternative solution) follow the same path of shrinking the lookup space.

I could add the simpler solution of:

def square_root(number):
    for num in range(number+1):
        if num * num == number:
            return num

But this isn't really related to Heron's method, IMO they're distinct methods.

As for a sum() solution, I can't think of an appropriate one. The two sum() community solutions linked above sum just one number from the range. The snippet linked just above is arguably an improvement on it.

[IsaacG]

Exercism markdown style is one sentence per line.