Quadratic coefficient matrices
Russell Walsmith
ixitol at gmail.com
Thu Jul 20 09:38:48 CEST 2006
A generalized Fibonacci sequence formula is the basis for the construction
of arrays from which quadratic coefficients are extracted. These sets map
into matrices, a step from which all sorts of discoveries derive. E.g.,
every ax^2 + bx + c has a complement (a – bk + ck^2)x^2 – (b – 2ck)x + c,
where a +/- root of one combines with a -/+ root of the other as a solution
to kxy + x + y = 0. See http://ixitol.com/QuadComs.pdf
This post is a bit off-topic perhaps, but there is clearly much left to be
discovered here... maybe even a sequence or two...
Ciao, Russell
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