Moderator Edit: This question provoked some discussion which, while off-topic, has the potential for interesting debate and further discussion. I have therefore copied the question to the Chat Room (so that the context of the discussion is not lost) and moved the off-topic replies to this thread. Please feel free to continue the off-topic discussion - in this thread.

If you have something to contribute regarding the solution, don't post it here. Post it at trigo-sum.

Calculate this sum :

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Is your calculator broken?

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calculators are boring

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Life is complex: it has both real and imaginary components.

I agree, but i'll tell you this: There's no way that I would spend any time with this sum analytically unless I was told that that is how it had to be done.

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This question is what I would say is an eighteenth century question still kicking around in the twenty-first century. There are just so many relevant problems that lead directly to being able to understand modern problems, why waste time on problems such as this?

I doubt the OP would be posting this question if all it required was punching some buttons on a calculator. I think you'll find that an exact value obtained without using technology is required.

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There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

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I knew that. I was trying to point out-in a very uneffictive way upon retrospect-that there was no hint toward a mode of approaceh to this problem.

Anywho, now that we've got this posted here we might as well discuss it. Plato ("The Apology" is my favorite) has taken the stance that solving this problem analytically is entirely a waste of time. I can't say that I disagree. I will say, however, that if we are to stop focusing on learning how to solve what has already been solved and allow technology to play larger and larger roles in pedagogy, this decision to do so must be made with the idea in mind of acheiving some higher goal. A pragmatic route to further enlightenment, if you will. An argument can indeed be presented-as Plato has already stated-that some things are just a waste of time. It's all about utiliy and time management. How can we rear the most useful and produtive society in the fastest possible way? Most certainly it is a matter of priorities. Allow the child to use the calcutator here, so that he will have more time to theorize there.

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VonNemo19’s first reply to the OP is rude and totally uncalled for. Look at the context in which the problem is being solved. If this problem is part of a larger and more important question, and you need an answer to it quickly, then by all means use a calculator. I agree that in such a case, toying with analytic methods would be a waste of time. However, if you are investigating a problem for its own sake, when you are interested not so much in the answer as in why the answer is what it is, then you don’t use a calculator. A calculator can only give you the answer, not insights into the anatomy of the problem. It is my belief that the latter is what is intended by the OP.

Also, I don’t think I can agree with Plato that investigating 18th-century problems is a waste of time. Some antiquated problems may be outdated in this day and age, but that does not mean that are no longer interesting, or even important. Why do you think schools still teach students how to prove that is irrational, or that there are infinitely many primes? These problems have been “solved” for over two thousands years, but why do we still bother with them? There are good reasons for this – it’s useful for sharpening the mathematical minds of young students, it’s interesting to see mathematics from the point of view of the ancient Greeks, and so on – and the same good reasons apply to the 18th century as to antiquity. Such problems are therefore far from being a waste of time.

So, we teach our children every problem there ever was? Or should we direct them towards where current problems are heading? Problem solving skills are highlydesirable traits to have, only if at the end of the day, we can use them to solve the right problem.

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The particular problems you cite are taught not from historical interest but because they lead directly to problems and/or techniques relevant today.

CB

Hello : - Ask this question in preparation for the Mathematics Olympiad in usa . THANKS

On the contrary, I think it can very well be taught from historical interest (as well as also being relevant to modern-day problems). Anyone studying or doing research into the history of mathematics will inevitably be interested in the way the ancient Greeks thought and reasoned mathematically, and will therefore be interested in studying the mathematical methods used by the ancient Greeks without reference to their applications to problems of later times.

We've strayed away from the question.

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Not on the contrary. I said nothing about how (the topics referred to in the post I was commenting on) they are/should be taught, just why they are taught. The motivation for teaching them is contemporary relevance.

There are many topics/problems that are not taught that are historically of interest but of little contemporary relevance.

CB

Way to bring it home there cap'n!

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