User talk:Neil Parker

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[edit] Discussion on Pythagorean triples

In the interests of possible further improvements on the page, may I humbly suggest that some careful thought be given to the slight contradiction posed by my contribution: namely that on the one hand the Platonic sequence is said to be a 'special case' of the general formula (m^2-n^2,2mn,m^2+n^2) with n=1 whilst on the other it can be shown that the 'general formula' itself may be derived from the Platonic sequence ([t^2-1]/2;t;[t^2+1]/2) when the parameter t is a rational number m/n.

That's not a contradiction – one of the triplets is just 2n2 times the other. BTW, I'm a little puzzled by this article. Is there some particular point you want to illustrate? The pictures are nice, but the article needs some sort of a wrapper around it, or something. It lacks focus as it stands. DavidCBryant 16:32, 28 August 2007 (UTC)

[edit] Duplicate images uploaded

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You don't need to sign articles you write, just things on talk pages and so forth. Cheers. Zelse81 07:14, 23 August 2007 (UTC)

[edit] Re: Diophantus II.VIII

  1. Thanks for your message. Re the adding/subtracting, the Latin runs "Communis adiiciatur utrimque defectus, & à similibus auferantur similia". A translation close to the original could read "I add the negative terms found on both sides, and similarly subtract the common [positive] term". The paraphrase by Bashmakova which I used spells out for the reader what the subtracted positive term (16) and the added negative terms (x2+16x) are. This has the advantage of making the mathematics clearer for the modern reader but the disadvantage, as you point out, of moving further away from the Latin text. If you think the disadvantage outweighs the advantage, I have no objection to using a closer translation.
  2. The problem with the use of Diophantine triple is that Diophantine triple is used to mean something else, viz., a triple of rational numbers such that the product of any two is one less than a square (cf. e.g. [1]. The reference here, in the numbering used by Heath (1885), is to Arithmetica IV.20.) Since (1; \frac{2t}{t^2+1}; \frac{t^2-1}{t^2+1}) will generate integral triples after clearing denominators, I believe the statement currently in the article is correct, with this clarification.
  3. For the role of t, in modern language, what is going on is that a Pythagorean triple is equivalent to a rational point on the unit circle, which, over the rational numbers, is birationally equivalent to the line. So, under a suitable birational equivalence (implictly found by Diophantus), any rational point on the circle gives a rational point on the line, which is t. Spacepotato (talk) 22:22, 26 November 2007 (UTC)

[edit] Duplicate images uploaded

Thanks for uploading Image:Droc Page20.JPG. A machine-controlled robot account noticed that you also uploaded the same image under the name Image:Page20.JPG. The copy called Image:Page20.JPG has been marked for speedy deletion since it is redundant. If this sounds okay to you, there is no need for you to take any action.

This is an automated message- you have not upset or annoyed anyone, and you do not need to respond. In the future, you may save yourself some confusion if you supply a meaningful file name and refer to 'my contributions' to remind yourself exactly which name you chose (file names are case sensitive, including the extension) so that you won't lose track of your uploads. For tips on good file naming, see Wikipedia's image use policy. If you have any questions about this notice, or feel that the deletion is inappropriate, please contact User:Staecker, who operates the robot account. Staeckerbot (talk) 09:59, 16 December 2007 (UTC)

[edit] Ptolemy's theorem

Please go back and fix your major new section to conform to normal heading case, and include citation of your sources. Dicklyon (talk) 19:39, 26 March 2008 (UTC)

Thanks for working on Ptolemy's theorem. It's still not clear to me how the reference relates to what you wrote. There's nothing in Hawking about sines, or not much anyway that I can find. It would be useful to have a footnote near the first intro of the interpretation from cut-the-knot, and a footnote for at least the first corrolary from Hawking, from Copernicus, etc. Let me know if you need help making footnotes; just explain to me what's from where. Dicklyon (talk) 05:01, 28 March 2008 (UTC)