The angle of inclination of several of the pyramids is in the range of 51.5 - 53.2 degrees. http://www.greatbuildings.com/buildings/Great_Pyramid.html Apparently, the Egyptians tried higher angles of inclination, but some of these pyramids collapsed -- e.g., Meidum. http://en.wikipedia.org/wiki/Egyptian_pyramids I would guess that the term "angle of repose" comes from the fact that these pyramids became graves? :-) :-) A pile of sand would not have the same shape _regardless of size_, as the increasing weight of the central part eventually changes the shape of the grains to cause a collapse into a smaller angle of inclination. And we in California are well aware that even relatively small amounts of water can cause spectacular collapses -- e.g., Route 1. At 09:01 AM 4/3/2007, Joshua Zucker wrote:

On 4/3/07, Simon Plouffe <simon.plouffe@gmail.com> wrote:

...

Hello,

I have this information about a certain constant associated with a pile of sand. Apparently the ratio of the half the base to the height is approx. 4/3.

I think the geological term you are looking for is the "angle of repose".

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I don't remember where I saw that for the first time, empirically, well at least for ordinary and dry sand, it looks like it is. In other words, a pile of sand will always have the same shape regardless of the size, or the slope is constant.

I read that the angle of repose for dry sand is about 30 degrees, but there are some other sites out there that tell me it depends on the grain size. With 30 degrees, that would be sqrt(3), not 4/3. But I think that's a pretty rough number, and I see numbers ranging up to just under 40 degrees, which would give a ratio of about 1.2, so your value of 4/3 seems to be in the range. The angle should be steeper for smaller sand particles.

--Joshua Zucker