(In reply to
re(2): Start the ball rolling...? by ed bottemiller)
History of problem:
Brian Smith put up a proble "Rectangle Around A Rhombus". While examining this with a spreadsheet I became aware that 119 and 120, as two legs of a Pythagorean triangle were one digit apart. I thenbegan to look for multiples of that, much like one would with a 3,4,5 triple (6,8,10; 9,12,15...).
K Sengupta pointed me in the direction of the link which is in my solution. It was only then that I realised that what I saw as an oddity was actually a little more common, eg (3,4,5), (20,21,29). It was from there "The defining equation is X^2 + (X+1)^2 = Z^2, which when doubled gives 2Z^2 = (2X+1)^2 + 1."
that the parameters arose thereby giving the structure for each term, with X being the base upon which a triple and subsequent multiples are based. We would lose base if we substituted as you have suggested, yes?
As for negative values, from where I was coming from they did not enter my thoughts; note a few comments prior to this one Dej Mar actually demonstrated this structure with some of those.
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Posted by brianjn
on 2008-05-09 22:45:01 |
re(3): Start the ball rolling...?
