On 1/10/07, kerry_and_ryan@xxxxxxx <kerry_and_ryan@xxxxxxx> wrote:

HOWEVER...
Taking such an approach is invalid, because it doesn't produce results that correspond to the published standard. If you start with 7/4" x 1" large, you should extrapolate a width of 4/7" for a 1" tall small. However the specified width of a small is 9/16".

And I see that as a rounding error. It's less than a two percent
difference (less than a hundredth of an inch in a pawn) but when you
start magnifying it (with larger 'mids) you'll start to see it.
A set of mathematically perfect 'mids would totally maintain its
aspect ratio (of 4:7). Anything less would be... wrong.
For reference:
9/16 = 0.5625
4/7 = 0.57142857142857142857142857142857
diff. = 0.0089285714285714285714285714285714
A lot of size standards have a "mathematically perfect" calculation
which is then rounded to a certain simpler value. International paper
sizes (for example) are based on the square root of two (an ugly
number in base ten decimal expansion) but are then rounded to the
nearest millimeter. If you assume that certain samples are /exactly/
the way they are supposed to be then certain properties break down as
you expand the standard. Meanwhile, the truth is that what you're
measuring is only an approximation.
So let's say this.
A pyramid is
(5+3x)/14 inches wide, rounded to the nearest 32nd and
(5+3x)/8 inches tall
where x is the number of pips.
Which gives us the currently published values AND makes the obsessive
mathematician in me happy.
--
- |) () /\/
and now I see that Carl's pretty much said the same thing so uh... thanks.