Talk:Brahmagupta-Fibonacci identity

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It is true this identity can be interpreted using norms for Q(i) but wouldn't it be more simple just to relate to the module property of complex numbers? It would also extend the property to real numbers. Since this identity is, as far as I know, generally used in the context of integer or rational numbers I would keep the norm comment also.Ricardo sandoval 06:41, 8 April 2007 (UTC)

I change the article accordingly but maybe the section "Interpretation via norms" can be compressed since its essentially the same as the relation to the complex numbers part. Ricardo sandoval 18:49, 29 April 2007 (UTC)

[edit] Not Correct

As I understand it, Brahmagupta's Identity is:

\ (x^2-Ny^2)(x'^2-Ny'^2) = (xx'+Nyy')^2 - N(xy'+x'y)^2

which is a generalization of an earlier identity of Diophantus:[1] The identity was used by Brahmagupta to generate solutions of Pell's equation.

Diophantus' Identity
\ (x^2+y^2)(x'^2+y'^2)=(xx'-yy')^2+(xy'+x'y)^2

Some one should correct this. Fowler&fowler«Talk» 14:21, 7 June 2007 (UTC)

  1. ^ Stillwell, John. 2004. Mathematics and its History, Springer, pp. 72-73
PS the identity can also be formulated by using the Brahmagupta matrix (although Brahmagupta, himself, didn't really define a matrix). Fowler&fowler«Talk» 14:27, 7 June 2007 (UTC)