On 3/3/07, Ryan McGuire <kerry_and_ryan@xxxxxxx> wrote:
Except that those formulas don't produce the "standard" dimensions as I understand them.
Yes they do. Check your math again.
Small 1 x 9/16
Medium 1 3/8 x 25/32
Large 1 3/4 x 1
Are these not the dimensions you started with?
Yes, that's all correct. When you round to the nearest 32nd (which is part of the formula), they're dead on. 4/7 - 9/16 ~= 0.0089 11/14 - 25/32 ~= 0.0044 That's about 9 or 5 /thousands/ of an inch. As you can see by the attached graph of calculated pyramid widths, they're pretty much the same until you get around 15 pips.
Given those dimensions, the formulae would be...
Height = (5 + 3x)/8
Width = (11 + 7x)/32
But that breaks down severely at higher pips and deforms your pyramids away from the beauty of the 4:7 ratio. -- - |) () /\/ I found an old copy of Maple I had in college, woohoo!
Attachment:
formula variation.gif
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