[Icehouse] The original pyramid size formula revealed!

[Andy Looney]

> > 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.

If intentional, it was only intuitively so, at least at first. The smalls 
are almost exactly the same size and shape as these 1-ounce lead fishing 
weights I got in the late eighties, which formed prototype #1. The other 
sizes started out arbitrarily bigger. The 3-ounce fishing weights weren't 
big enough so Larges got bigger during the first few prototypes until they 
"felt right."

> Nah, I don't think so. I suspect that the Small Height = Large Base and
> the (arbitrary?) Height = 7/4 Base was enough.

Actually, Small Height = Large Base was something we just noticed one day. 
Sometimes things just work out magically, like the fact that 2 smalls 
stacked are exactly as tall as a medium. That wasn't planned, it worked out 
that way because of the wall thickness. The wall thickness was chosen to be 
as thick as possible and still allow the pyramids to nest.

> 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?

Sorry I guess I didn't realize this was keeping people up at night... I 
have a hard time keeping up with all the email, and I was thinking you-all 
were just having fun yammering about equations that make my eyes glaze 
over...

> 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! ;)

OK, having been called out, I've dug into the oldest of files to uncover a 
document vital to this conversation. It's called "An Odd Letter From Kit To 
John," and it's dated 8 March 1990. Wow how time flies.

This is an amazing 5-page letter filled with hand-drawn diagrams and graphs 
and charts and equations. Perhaps later I'll scan in and post the whole 
thing. Here's how it begins:

"John: Since a few days after I got my Icehouse set, I've been wondering 
what was on your mind as you determined piece size. I've come to the 
conclusion that a small man on crutches helped you -- and he held one 
crutch in his mouth and one under his arm and he computed pyramid size."

Now, remember, this was in 1990. The set he was evaluating was one of the 
original 100 hand-poured plastic sets, not the factory-made stackable 
beauties we sell now. The original pieces had Larges and Smalls that were 
very close to the current standard, but the Mediums were too big.

The conclusion of Kit Cooper's memo is a set of recommendations for what he 
thought we were after, and his calculations set the standard we now use. He 
writes:

"Of course, it is obvious that possibility (2),(C) is the correct choice. 
Not only do the pyramid Base Size and Face Height vary with a neat 
equation: BS = 4 / 7 FH = (4 + (2 ^ (PointValue - 1)) / 8, but the pyramids 
are similar too."

So there you go, the formula we used. I hope this clears things up. Sorry 
about the angst.

-- Andy