Looney Labs Icehouse Mailing list Archive

Re: [Icehouse] Re: Isosceles triangle angle

  • Fromkerry_and_ryan@xxxxxxx
  • DateTue, 06 Mar 2007 17:05:18 +0000
>From David Artman:
>BUT... I haven't seen anyone else derive the Base from the
> previous piece's Base. That's where I think all these other
> formulas go wrong: they are looking for a consistent formula
> for any given pip count X, but I do not think that is how
> they were originally invented. But by going *just* on what's
> been published about dimensions for 1, 2, and 3 pips, and
> suspecting that the 1 Height = 3 Base is the *only* intentional
> relationship; I think Base(x) = Base(x-1) + 0.21875 is the best
> way to figure any other sizes.

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

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.

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.