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I’ve recently become interested in rational right triangles — especially the relationship between their geometric and algebraic properties and possible applications to the solutions of Diophantine equations.

I’ve read the “basics” (relevant sections of compendia such as Dickson’s History; introductory chapters of advanced geometry texts; individual papers found through JSTOR; etc.), and now want to see some really in-depth works.

Hence I want to ask “What are the best books/papers on the properties of rational right triangles?”.

  1. Is that type of question appropriate on MSE? It’s almost certainly going to lead to lots of discussion and answers/comments, and can’t really be answered precisely (the way, for example, a question about a specific math problem can be).
  2. In light of the above, I thought it should be a “community wiki” question… But that box has been eliminated globally, and a quick search of this site shows me that CW is a touchy subject.

How should I proceed?

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  • $\begingroup$ I added the tag "specific question," this focuses the post a bit more on your particular question. If you prefer the discussion to be more open, please feel free to remove it. $\endgroup$ – quid Aug 19 '16 at 19:20
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    $\begingroup$ Speaking for myself, acceptance of such questions depends on $X$ being a research level topic, not a topic (as I perceive rational right triangles to be) which has been thoroughly understood for hundreds of years. Possibly you have in mind a quite novel "property of rational right triangles" that would amount to a research level topic, in which case I'd be open to your asking a question about that. But the framing of your (meta)Question seems to be in expectation that material resolving your problem is to be found in the (current) literature. $\endgroup$ – hardmath Aug 20 '16 at 2:53
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    $\begingroup$ @hardmath: I am currently examining something which is either trivial or would turn into a research level topic which has never been examined, as far as I can tell. But I can't tell that until I see all the high-end publications on the topic. =) $\endgroup$ – Kieren MacMillan Aug 20 '16 at 11:40
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I'd avoid the word 'best;' it just causes the problem of subjectivity and does not bring much precision in return.

You search for references in a relatively specific subject. Explain in a bit more detail than you did already what it is about and what you have read already. Then, ask for additional references to further your studies in this direction. Try to explain specifically what you are looking for. If you have an old paper on some topic, you might ask for developments in this direction. If you know a particular type of advanced tool is used, you might want to ask about papers using it. Etc.

For the most part users will anyway recommend the sources they find "best" on such a question.

For a general view on this, I like this answer.

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In addition to quids excellent answer.

Is a question about “Best books/papers on X” appropriate?

1.) You should define what is best for you.

  • Best in the sense of most popular?
  • Best in the sense of most exhaustive?
  • Best in the sense of most succinct?
  • Best in the sense of best suited for solving problem Y?
  • ...

We need context and objective criteria.

2.) X should be sufficiently specific.

Otherwise possible answers could easily be too broad. Try to include information which information should be included and which can be left out. Also specify if you want overviews or in-depth material.

Summary: Context matters a lot and make questions answerable and useful for others. Include your specific needs in the question and you'll get meaningful recommendations.

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