Simon writes: << 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 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. Is there anybody that has any information about this phenomena? Is this known ?
Thanks to the title of a noel by Wallace Stegner, I learned that the angle of the steepest pile of [whatever] is called its "angle of repose"; here it would be atan(3/4). (Cf. < http://en.wikipedia.org/wiki/Angle_of_repose >.) The angle depends heavily on the kind of stuff that is piled up. The angle of repose would be low for glass marbles, and higher for gravel of about the same size. So I doubt that the number for a pile of sand is intentionally trying to be 3/4 (or any fraction with a small denominator). --Dan