The Dirac-Fuchs Theorem is a formula that calculates the mean chord of a shape that was proved by Paul Dirac and Klaus Fuchs while they were both working on the Manhattan Project.


z = the mean chord
V = the volume of the shape
A = the surface area of the shape

For example, the mean chord of a cube is two thirds of the edge length.

This formula is only valid for three-dimentional convex shapes in euclidean geometry. However, many concave shapes can be modeled locally as convex allowing good approximations to be made.

The formula is key for the functioning of the atomic bomb; the point at which fissile material goes super-critical is not dependent on the mass as normally thought, but upon the mean chord of the piece of uranium. That means it is possible to have a material with more than the critical mass not to set off a chain reaction if it is in the wrong geometrical shape.