### inverse square law

(a value's dependency upon reciprocal of the square of the distance from something)

An **inverse square law** is a scientific law (i.e., well-established
model) asserting that some value depends upon the distance from
something, more specifically on the reciprocal of the square
of that distance (1/d²). If that *something* is a point or spherically
symmetric body, then given any distance (i.e., the radius of
a sphere centered on the point), the sum (integral) of the
value across all points at any such distance is the same.
An inverse square law generally
implies three-dimensional Euclidean space,
and serves as an approximation if the space is close to that,
such as are current models of the universe.

Some common inverse-square examples:

- The density of
*things*, e.g., particles, sprayed in all directions (or covering some specific solid angle) from a point.
- Electromagnetic radiation (EMR), similarly, from a point source.
- Sound waves from a point source.
- Gravity.
- Electric force, e.g., associated with an electron or proton.

Phenomena that are *not* inverse square:

- The height of spreading ripples in a pond, e.g., from where something dropped into it. The ripples spread over just 2 dimensions instead of 3 and the height is related to 1/d rather than 1/d².
- gravitational waves, also 1/d, more like ripples in a pond than like EMR or sound waves.

(*physics,mathematics*)
http://en.wikipedia.org/wiki/Inverse-square_law

**Referenced by:**

Coulomb's law

electric field (E)

gravitational field

gravitational wave (GW)

Legendre polynomials

N-body simulation

strong force

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