[Icehouse] Pointless Pedantic Pursuit of Proper Pyramid Proportions

[Don Sheldon]

On 3/5/07, Robert Bryan <rbryan at extendthereach.com> wrote:
> This post continues the ultimately pointless discussion of larger size
> pyramid dimensions which I somewhat knowingly set off in my previous
> post.  To those who find such discussions annoying, I offer my apologies
> and encourage you to skip the rest of it.  To those who find them
> interesting, but disagree with me, please accept my forthcoming outrage
> in the good humor with which it is intended. :)

I'm going to keep this paragraph here as a header and say "ditto."

> > When you round to the nearest 32nd (which is part of the formula),
> they're > dead on.
>
> When you round they're dead on?  I find this both unsurprising and
> unsatisfying.  My proposed formula
> requires no rounding whatsoever; and produces exactly the correct sizes
> for the existing pieces.

I will counter with an interesting (to me) fact that such rounding is
often used in descriptions of standards.  International sized paper
(A4, A3, etc.) is defined as having edges with a ratio of 1:sqrt(2)
and areas that are 1/(2^n) square meters.  But, officially, these
measurements are always rounded to the nearest millimeter.

So A0 (with an area of 1 square meter) IS NOT the wacky transcendental
numbers that you might calculate, it is, in fact 1189mm x 841mm
/exactly/, no more, no less.

Point being, there is precedent for these kinds of formulae.

http://en.wikipedia.org/wiki/A4_paper_size

> > But that breaks down severely at higher pips and deforms your pyramids
> > away from the beauty of the 4:7 ratio.
>
> Severely? It converges on 7:12, which is roughly 2% different from 4:7.
> So it would be hard to say 4:7 was aesthetically pleasing but something
> between that and 7:12 was not.  For the same reason, you can easily be
> forgiven for being lured into the heresy that it's all about the 4:7
> ratio.  The 1 and 2 pointers are not 4:7, though they easily could be
> were that the mystically desirable ratio. Clearly, it is all about the
> steady convergence from 11:20 to 7:12.

It's true.  There isn't a huge difference.  Certainly not enough to
warrant a serious conversation of this magnitude.  Lucky for us we're
not serious.

And ewww, steady variation of aspect ratios?!  How appalling!

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