On 3/5/07, Robert Bryan <rbryan@xxxxxxxxxxxxxxxxxx> 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! -- - |) () /\/