-------------- Original message ---------------------- From: Christopher Hickman <tophu@xxxxxxx> > On Wednesday, January 10, 2007, at 02:36PM, "Christopher Hickman" > <tophu@xxxxxxx> wrote: > >On Wednesday, January 10, 2007, at 02:05PM, "Don Sheldon" > <don.sheldon@xxxxxxxxx> wrote: > >> And I think that IS linear growth, pretty much by definition. > > > >Yeah. You're right. I realize now what I thought I meant: the angles are not > constant. As the pyramids > > get bigger, the get more squat (that is, the linear growth of the base width > is a larger ratio to the linear > > growth of the height). So, if you were to take a hypothetical 10 pointer and > cut of the top 1 inch of the tip, > > it would NOT be a 1 pointer, because it would be waaaay too wide. > > Ok, so this is just completely wrong. The linear progression is good for both > the dimensions and the angles. Here's a pdf that has an illustration of a > (theoretical) ten pyramid nest, from a zero pip to a nine. Just view it at 100% > and there's your size comparison. So I still think a "jumbo" set of 4-6 > pointers would be sweet. > > http://homepage.mac.com/tophu/Pyramids0-9.pdf > _______________________________________________ > Icehouse mailing list > Icehouse@xxxxxxxxxxxxxxxxxxxx > http://lists.looneylabs.com/mailman/listinfo/icehouse I'm not exactly sure which approach you're say is just completely wrong, but if I understnd you correctly I would have to disagree. My stance: The widths make a linear relationship with pip count. The heights make a linear relationship with pip count. Pyramids DO get squatter/less pointy as the pip count goes up. (The top 1" of a hypothetical 10-pointer would be too wide to be a small.) The angles do NOT make a linear relationship with pip count. I'm basing my calculations on these dimensions: Small: 1" x 9/16" Medium: 11/8" x 25/32" Large: 7/4" x 1" ...as published at http://www.wunderland.com/icehouse/MakingIcehouse.html If, on the other hand, you start with the 7/4" x 1" size of a large plus the 1" height for a small and then inter/extrapolate from there to get the other dimensions, then OF COURSE the heights and widths make linear relationships with the pip count exactly BECAUSE that's how you calculated them. Also, in that case any set of corresponding angles wouldn't just make a linear relationship, they would make a CONSTANT relationship with the pip count. 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". Ryan