π.R2 Square Radius Law - JulTob/Mathematics GitHub Wiki
Many phenomena in nature follow the principles of what we call $\color{Silver}β Theβ Squareβ Rootβ Law$.
- Gravity
- Light's spread
- Electric Field's intensity
These effects arise similarly because of the three-dimensional nature of our universe.
Absent a specific dimensionality, imagine you had a source of energy (or matter) it would spread away from the source. (A sink would pull energy towards itself.)
In a $0Dimensions$ Universe energy could no spread, so it would concentrate in a $0D$ point of origin.
π΅
π’
π‘
π
π΄
π£
βͺοΈ
In a $1D$ world energy could spread in the line universe, from the source point as an origin.
π’
β«βββββββββββββββ R
π’π’π’
β«βββββββββββββββ R
π’π’π’π’π’
β«βββββββββββββββ R
π’π’π’π’π’π’π’
β«βββββββββββββββ R
π’π’π’π’π’π’π’π’π’π’π’
β«βββββββββββββββ R
Therefore, a source of intensity $I$, creating $I$ elements (energy, matter, money...) per unit of time would spread this intensity only in linear path(s).
One example of these sources are batteries in circuits, that create a constant supply of electrons. Or a river's water conducted for irrigation.
The different paths in a circuit or 1D-source keep an equal amount of intensity distributed from the source into the different paths in (likely different) proportions
\color{#A6A6A8}
I = β I_n = β \frac{I}{R_n}
2D Flatlands
In a $Flatland$ of 2Dimensions the source distributes from the center in radial directions.
If we imagine these units being created in small quantities in the focus, as they are created they push out radially, as a fountain making ripples. The Energy Dispersion follows the circle itself as it expands
π€π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π€
π΄π΄π π π π π π π π π π΄π΄
π΄π π π‘π‘π‘π‘π‘π‘π‘π π π΄
π΄π π‘π‘π’π’π’π’π’π‘π‘π π΄
π΄π π‘π’π’π΅π΅π΅π’π’π‘π π΄
π΄π π‘π’π΅π΅π£π΅π΅π’π‘π π΄
π΄π π‘π’π΅π£βͺοΈπ£π΅π’π‘π π΄
π΄π π‘π’π΅π΅π£π΅π΅π’π‘π π΄
π΄π π‘π’π’π΅π΅π΅π’π’π‘π π΄
π΄π π‘π‘π’π’π’π’π’π‘π‘π π΄
π΄π π π‘π‘π‘π‘π‘π‘π‘π π π΄
π΄π΄π π π π π π π π π π΄π΄
π€π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π€
π’
β«βββββββββββββββ
π‘π’
β«βββββββββββββββ
π π‘π’
β«βββββββββββββββ
π΄π π‘π’
β«βββββββββββββββ
βͺοΈπ£π΄π π‘π’
β«βββββββββββββββ R
In this kind of universe, the distribution of this Intensity is distributed in circles centered at the origin. The next circle is one bit weaker than the one before, following a linear inverse.
\color{#CECECE}
\frac{I}{R}
In 3 Dimensions
π΄π΄π΄π΄π΄π΄π΄
π΄π΄π΄π΄π΄π΄π΄π΄
π΄π΄π΄π΄π΄π΄π΄π΄π΄
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄
π π π π π π π΄π΄π΄π΄π΄π΄π΄
π π π π π π π π΄π΄π΄π΄π΄π΄π΄
π π π π π π π π π΄π΄π΄π΄π΄π΄π΄
π π π π π π π π π π΄π΄π΄π΄π΄π΄π΄
π π π π π π π π π π π΄π΄π΄π΄π΄π΄π΄
π‘π‘π‘π‘π‘π π π π π π π΄π΄π΄π΄π΄π΄π΄
π‘π‘π‘π‘π‘π‘π π π π π π π΄π΄π΄π΄π΄π΄π΄
π‘π‘π‘π‘π‘π‘π‘π π π π π π π΄π΄π΄π΄π΄π΄π΄
π‘π‘π‘π‘π‘π‘π‘π‘π π π π π π π΄π΄π΄π΄π΄π΄π΄
π’π’π’π’π‘π‘π‘π‘π‘π π π π π π π΄π΄π΄π΄π΄π΄π΄
π’π’π’π’π’π‘π‘π‘π‘π‘π π π π π π π΄π΄π΄π΄π΄π΄
π’π’π’π’π’π’π‘π‘π‘π‘π‘π π π π π π΄π΄π΄π΄π΄π΄
π΅π΅π΅π’π’π’π’π‘π‘π‘π‘π π π π π π΄π΄π΄π΄π΄π΄
π΅π΅π΅π΅π’π’π’π‘π‘π‘π‘π π π π π π΄π΄π΄π΄π΄π΄
π£π£π΅π΅π’π’π’π‘π‘π‘π‘π π π π π π΄π΄π΄π΄π΄π΄
βͺοΈπ£π΅π΅π’π’π’π‘π‘π‘π‘π π π π π π΄π΄π΄π΄π΄π΄
βͺοΈπ£π΅π΅π’π’π’π‘π‘π‘π‘π π π π π π΄π΄π΄π΄π΄π΄
β«βββββββββββββββ R
In this scenario, the source of Intensity will distribute this "energy" radially in a sphere's surface.
\color{#E8E9F3}
\frac{I}{R^2}
Generally, and determining
As we have seen, every level of dimensionality means the distribution of this abstract $Intensity$ is distributed radially in all possible directions.
As it distributes, the intensity is reduced as if distributed in the border of an imaginary chape that expands radially. We conclude that this intensity measured at a point is then proportional to the inverse of the BORDER of this shape.
\color{#CECECE}
\frac{I}{βShape}
As we have generalized this behavior in any dimension we can determine in how many dimensions we inhabit by measuring effects as they distance from the source.
We can measure the Intensity as we increase the distance to the source. We then determined that the forces of Electrostatics and Gravity, the spreading of light, or explosions of pyrotechnics, are consistent with a 3D universe.