e to the pi i..........= - 1.............the "seemingly innocuous" equation x squared = - 1.............when values of the roots of i..............are plugged in for x.........u get interesting results.......spin.........a number with a negative exponent................flips........spins...................x to the negative 2.........is 1/ x squared.................

Formula[edit]

Mathematically notated :

${\displaystyle {\text{intensity}}\ \propto \ {\frac {1}{{\text{distance}}^{2}}}\,}$

It can also be mathematically expressed as :

${\displaystyle {\frac {{\text{intensity}}_{1}}{{\text{intensity}}_{2}}}={\frac {{{\text{distance}}_{2}}^{2}}{{{\text{distance}}_{1}}^{2}}}}$

or as the formulation of a constant quantity :

${\displaystyle {\text{intensity}}_{1}\times {{\text{distance}}_{1}}^{2}={\text{intensity}}_{2}\times {{\text{distance}}_{2}}^{2}}$

The divergence of a vector field which is the resultant of radial inverse-square law fields with respect to one or more sources is everywhere proportional to the strength of the local sources, and hence zero outside sources. Newton's law of universal gravitation follows an inverse-square law, as do the effects of electric, magnetic, light, sound, and radiation phenomena.

Justification[edit]

The inverse-square law generally applies when some force, energy, or other conserved quantity is evenly radiated outward from a point source in three-dimensional space. Since the surface area of a sphere (which is 4πr² ) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source. Gauss's law is similarly applicable, and can be used with any physical quantity that acts in accord to the inverse-square relationship.