> A few things:
> 1. Your formula needs a starting point, perhaps something like...
> Base(x) = [ 0.5625 ; if x=1 (or maybe you want to start at x=0 or -1)
> [ Base(x-1) + 0.21875 ; if x!=1
Well, fair enough; it's good to be thorough. :)
> 2. That recursive formula is equivalent to the standard...
> Base(x) = 0.34375 + 0.21875*x
> I could prove that by induction if you want to see it.
I didn't know that standard. I guess I haven't innovated anything at
all, then.
> 3. I would bet that the Height(3)-Height(2)=Height(2)-Height(1) and
> Base(3)-Base(2)=Base(2)-Base(1) were intentional relationships.
Nah, I don't think so. I suspect that the Small Height = Large Base and
the
(arbitrary?) Height = 7/4 Base was enough. Medium dimensions are just,
well, the median values between the smalls and larges. Divide by two
(for symmetry) and you get--not surprisingly nor intentionally but
merely
automatically--your Bases statement above. The Heights merely follow
from the 7/4 ratio.
But whatever. Are we done, yet?
----------
Out of curiosity, does Andy get some perverse pleasure from watching
us speculate about this trivia? Or is he utterly unaware that this
is a repeating point of debate and contention? Or is there some kind
of "preserving the mystery" balderdash behind it all? (Obviously, we
are going to crush the life out of the mystery, grinding away at trig
and ratios and recursive formulas; so what's left to preserve, and what
is the cost in time and frustration, while that minute "mystery" is
preserved?
Yeah, I'm calling you out, bub! Pick one of those above, indefensible
reasons for not telling us what the deal is; or spill it, Andy! ;)
David