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https://en.wikipedia.org/w/index.php?title=Formulas_for_generating_Pythagorean_triples#Dickson%27s_method

As in the title. Or does anybody did it? Thanks in advance for your replies.

Adam 'Palermo' Stankiewicz
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    I'm quite sure Dickson proved this. The wikipedia page you link to references a recent proof in the literature. – Ethan Bolker Oct 11 '19 at 20:41
  • I'm supposing, you not quite well understood me. I know, there are proofs of his method (especially short one, given by Rukavicka of Prague Tech University), but my question is about from where these formulas came from. – Adam 'Palermo' Stankiewicz Oct 11 '19 at 20:46
  • Presumably Dickson invented them. How mathematicians figure out new mathematics is an interesting question, but not a mathematical one. – Ethan Bolker Oct 11 '19 at 20:48
  • OK, but I came out to this formulas (to be precise: equal formulas) by a simple calculus from undeniable characteristics of Pythagorean triples/triangles. So: not, by 'inventing' them, but by calculating them. And I'm wondering if I should write a scientific-grade paper on this topic, or not (to not 'discover Africa' again, you know: crocodiles in Limpopo river etc.) ;) – Adam 'Palermo' Stankiewicz Oct 11 '19 at 21:02
  • If you have a new clever way to arrive at these formulas you may be able to publish a short paper ob your work. There are journals (some for students) that accept good short papers on topics like this one. Your contribution would have to be unusual and really well written to be publishable. In general , rediscovering essentially elementary things is fun to do but does not usually lead to a "scientific grade" paper. – Ethan Bolker Oct 11 '19 at 21:10
  • @EthanBolker I'm from Poland and I'm not from scientific community... so could you be so kind to give me advice about what journals could be a good target for that matter? Thanks. – Adam 'Palermo' Stankiewicz Oct 11 '19 at 21:16
  • Here's one well respected place. Ypu'll need some kind of library access to see current issues of Mathematics Magazine or the College Math Journal. I don't know about older ones https://www.maa.org/press/periodicals . You can try a google search for elementary or high school or recreational math journals. – Ethan Bolker Oct 11 '19 at 21:37

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Alright, page 169 in volume II of his History. He published it in the first year of the American Mathematical Monthly in 1894. Apparently that article was a single page, perhaps it was in the form of a letter. Dickson then lists four people who found the same description later, published 1897, 1901, 1908, 1916.

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Will Jagy
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  • Thanks for your well directed reply. It took me some amount of time to check matter you wrote about, but there is still some uncertainty: pp. 165-170 describe shown/known (in 1920's) methods of solving x^2+y^2=z^2, but because I haven't access to cited sources, so I still do not know if somebody drawn/calculated (1) [p. 165], or in some way 'guessed' it and then, eventually, proved it... Now I believe, the only solution would be visiting the Library of Congress ;) – Adam 'Palermo' Stankiewicz Oct 13 '19 at 20:41