Solid angle is much, much farther away. The solid angle subtended by the complete ()-dimensional spherical surface of the unit sphere in -dimensional Euclidean space can be defined in any number of dimensions . One often needs this solid angle factor in calculations with spherical symmetry. It is given by the formula where is the gamma function. When is an integer, the gamma function can be computed explicitly. It follows that This gives the expected results of 4 steradians for the 3D sphere bounded by a surface of area and 2 radians for the 2D circle bounded by a circumference of length
Menger sponge itself is the limit of this process after an infinite number of iterations. The "n"th stage of the Menger sponge, "M", is made up of 20 smaller cubes, each with a side length of (1/3). The total volume of "M" is thus (20/27). The total surface area of "M" is given by the expression 2(20/9) + 4(8/9). Therefore the construction's volume approaches zero while its surface area increases without bound. Yet any chosen surface in the construction will be thoroughly punctured as the construction continues, so that the limit is neither a solid nor a surface; it has a topological