3D Exponential Constant = 2.73

The number "e" = 2.73 is an interesting number and in Calculus explored as a Limit of small increments to 1 raised to Infinity.

In Nature, the packing of Spheres is most efficient when 6 Spheres as in Soddy Hexlet are formed in center, and 3 in Top and 3 in Bottom, but in reverse polarity - the arrow formed with 3 is opposite in directions.

This packing is called HCP and 12 Spheres surround 1 Sphere - the source of Energy.
This is not taught in Physics but I came to conclusion that the Energy propagates through Geometrical-Arithmetic Inversions - and also confirmed by 18th Century Mathematicians and Physicists who solved Differential Wave Equations.  This also involves Geometric and Arithmetic Progressions.

In case of Light, I have also seen Harmonic Progressions.

Geometrically basically the inner circle catches on to the outer sphere through process of inversion, so 1 Sphere now becomes a bigger ball of 13 Spheres, and so on.

Now if one takes the Energy Differential and Density calculation, one would also approach the number 2.72 but in 3 Dimensions!