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Re: Volume of a Geodesic Dome
Posted:
Jul 8, 1995 5:06 PM


In article <Pine.SUN.3.91.950629162842.8995K100000@mace.Princeton.EDU>, John Conway <conway@math.Princeton.EDU> wrote: > >On 28 Jun 1995, Your Name wrote: >> Can any one describe for me how one would determine the volume of a >> geodesic dome as a function of the number of sides it has? I've made the >> assumption that all the sides are triangular with 60 degree angles. >>  Jason Acker >> > I'm afraid that there's no real answer to this question, because >"geodesic domes" vary in shape. Also, it's seldom the case that >all the triangles have the same shape; if you look carefully at the >next one you see, you'll see they have slightly different sizes and >shapes, and aren't all equilateral. ... > (base times height)/3
John's comments are certainly valid, but I'd just like to point out that we can estimate fairly well the volume of a geodesic dome made of a large number N of triangles, each of which is nearly equilateral (say all the side lengths are close to 1).
The total area of this dome will be $N\sqrt{3}/4$, if it is approximately a sphere of radius $r$, then we must have $4\pi r^2 \approx N\sqrt3/4$, and volume approximately $4\pi r^3/3$. We can solve for r and see that this volume is about (N \sqrt{3})^{3/2} / (48 \sqrt\pi)
John Sullivan



