Green's theorem:
Green's theorem has several mathematical relationships depending upon who is doing the writing. The relationship here is the vector analysis between double and triple integrals as it applies to Gauss theorem in vector form. Where the integrations are to be carried out over the volume and surface, let F be a vector function and v a volume bounded by a surface s:
Generally, Green's theorem with u & v are scalar functions, S indicates a double and T a triple integral:
This is a fancy way of saying if you know what the segments of a sphere's volume are, you know the surface too.
Stokes theorem: Let F be a vector function and s a surface bounded by a simple closed curve c where 
. Where dl is taken only on the perimeter of the surface.
H is the magnetic field intensity and as Stokes Theorem applies to magnetic:
Ampere's Circuital Law:
The line integral of H about any closed path is exactly equal to the current enclosed by that path:
Maxwell's equations: Maxwell's electromagnetic wave equation in terms of a wave of angular velocity function s = j , a magnetic field, electric field and vector operator:
Biot-Savart law:
At any point P, the magnitude of the magnetic field intensity produced by a differential element is proportional to the product of the current, magnitude of the differential length and sin of the angle lying between the length and point P and inversely proportional to the square of the distance. The direction of the field is normal to the plane of differential element and the point.
Thus;
Applying the definitions of J as current density, K as surface current density with s as the surface, and v as the volume, it can be shown that I dL = K ds = J dv. Then alternate forms of the Biot-Savart law are:
SQUARE LAW or INVERSE SQUARE LAW. However you want to look at it.
At this time it is possible to start to develop a constant relationship between force, distance, flux, and time. The total basis of this relationship is the fundamental mathematical relationship of an uniform volume to its area. There is only one uniform volumetric body and that is of a sphere. All other bodies are nonuniform.
A sphere is the only volumetric body which will allow itself to be described by one single point and an infinite sum of vectors with all the same magnitude integrated through three dimensional space.
This is the basis to Einstein specialized time relationships. The mathematical relationship of a spherical body is extremely important. A mental picture between all the known facts about energy, electromagnetic radiation, electrical fields, magnetic fields and force and spherical space must be developed. The special mathematical relationship is that of the change of the area of a sphere for a change in the vectored magnitude.
The square law or inverse square law, as it many times stated, approximates radiating field decreases or increases in area strength is by being proportional to the square of the distance ratio. If Area A1 had a radius r1, and area A2 had a radius of r2, the relationship of A2 / A1 would be (r2 / r1)^2. For any energy intensity radiating spherically as the area of incidence increases, the density decreases by change in area. The area of a sphere is 4 * 
* r^2.
Momentum or kinetic energy = 1/2 * m * v^2; m = mass, v = velocity.
Distance from a straight drop. Distances = 1/2 * a * t^2; a = acceleration, t = time.
Angular momentum = 1/2 * I * ^2; I = inertia, = angular velocity.
Energy in a capacitor = 1/2 * c * V^2; c = capacitance, V = voltage.
Magnetic energy = 1/2 * æ * B^2; æ = permeability, B = magnetic induction.
Albert's E = m * c^2; m = mass, c = speed of light.
These are examples of the unique condition of nature called the square law. It is not important if it is the inverse square law or the square, the effect on an area density of a flux is all the same thing. Density distribution is based on two spherical objects of different radii with the exact same origin.
SUPERSYMETERY
Supersymetery seems to relate radiation concepts to mass attraction concepts. In general one can relate the three dimensions of space, the one dimension of time with another dimension of type. Thus, making the order of nature at least 5 dimensions. Many theoretical physicists believe there are many more dimensions which make up existence. When evaluating the supersymetery equations there becomes evident of a rule or law of nature. Which is: In the evaluation of a real multidimensional matrix one can only use nonvanishing matrix elements when representing real occurrences.
Supersymetery is a development which refers to a spherical vector. A spherical vector is the same as a standard vector except there is a set of infinite vectors with the same magnitude and origin but different directions. Because each vector has a different direction they are different vectors but they are viewed as a whole. For any given symmetrical system velocity moving out symmetrically from a point source any number of symmetrical nonvanishing conditions can exist. V is the vector in any of infinite 360 by 360 degree integration where W1, W2, ... Wi are real. Wl being any angular vector.
Typically, the change of state for any physical system was give by:
Now, the change of state for any physical system is not purely physical. The change of state must contain the terms for rotational inertia, gravitational affects of near by objects, the affects of charge and magnetics. The new change of state is given by:
Obviously, this type of function can be very complex. Then when one adds the complexity of vectors and time, this becomes a very cumbersome problem. The affects of three dimensional space in a system which must maintain a constant equilibrium is spherical and very symmetrical. The symmetrical nature of a sphere tends to help evaluate this complex function.
GEOMETRIC SERIES
The series:
is said to be a geometric series if each term after the first is a fixed multiple of the term before it; that is there is a number r called a ration of the series such that:
ZEROTH ORDER SET
Zero is a totally unique number in that it can not be represented by a power function nor can any other number be divided by zero. Zero is a real number and a lot of times it is the first occurrence of a set. For a binary set of magnitude 1, the progressive order is 0 & 1. If zero is a valid state in a valid function, then for the progression of that function which zero is valid F(x) for x = 0, 1, 2, 3, 4, 5...n becomes:
Zeroth order for a binary system^:
Adding zero doesn't change the sum only the first term in the series. When dealing with a geometric series this would reset the series to:
The zeroth order set makes the first zero term real. The zeroth order system comes from taking a variable and raising it to the zeroth power. In classical mathematics, zero raised to the zeroth power is undefined. For example; given a variable N and raise it to a set of powers form -3 to +3. This would give the sequence:
Should N be 0 the any number divided by 0 is infinite and undefined. In classical mathematics, even 0/0 is undefined. But, by empirical solution we find that the limit of N to the zeroth power is 1. 10^0=1, 1^0=1, 0.1^0=1, 0.00001^0=1....
NATURAL FUNCTION & PI
The basis for natural log is base "e." Although this will seem any thing but natural it really is a good number. "e" is like ã in that it is transcendental. The value "e" is defined as the limit of:
PI = = circumference /diameter = 180 degrees = 3.141592653589793238462.
It should be noted that both and e have an infinite nonrepeating set of numbers and in many astronomical calculations its best to use 21 places. It takes 16 places just for the beginning power-drag relationship of this theory to be seen.
EULERS IDENTY
TABLE OF CONTENTS