Brunardot's Theorem: A Proof of "One"

By definition: the theory of Reality, its principles,
and its corollaries,
must be simple.

The most simple is the most complex;
thus . . . the most complex is
the most simple.

The Brunardot Theorem states that when:

v = ep² for the ellipse c² = 2v² - s²
a certain class of ellipses is created that determines the fundamental principles of number theory and Nature;

where, c = a major chord;
e = epsilon, the Elliptical Constant;
p = a perigee; s = a soliton; and v = a vector.

A corollary states that:

p, s, v, and a, the apogee,

are the first four terms of a generalized Fibonacci series.

When p and s are Natural integers the Brunardot Golden Corollaries result when

the terms of said generalized Fibonacci series

are those of the Brunardot Series.

The Brunardot Series is a generalized Fibonacci series

that has a Natural Integer for the second term and

the third term is the square of the first.

	The formula:
	c² = 2v² - s² describes a Fibonacci ellipse, where
	"c" is the length referred to as the Brunardot chord.
	"v" is the length referred to as the vector; and,

	"s" is the length referred to as the soliton;
	A Conceptual ellipse (CE) is a Fibonacci ellipse, which is generated for every Natural integer value of "Tau"; and, all Conceptual ellipses have a unique Natural Prime number for the diagonal, "d"; and, the following segments, as is the diagonal, are all Natural integers with values expressed in Natural Units, "U":

	Most notably! . . . four basic components of every Conceptual ellipse, (CE), are consecutive terms of a Fibonacci series. The components, in sequence, are: the perigee, "p"; the soliton, "s"; the vector, "v"; and, the apogee, "a."
	A Brunardot ellipse (BE) is defined as:

Any Conceptual ellipse (CE) that has the
force, "F," as a Natural integer.

Brunardot Harmonic Ellipses (BHE) are defined as:

An unending series of Brunardot ellipses (BE)
that are generated by any, single, Natural integer; and,
have the vector "v" and the radius "r" as
squares of integers; and with the
diagonal "d," Brunardot Integer "i," and perigee "p"
as Natural Prime numbers.

Conceptual triangles describe Conceptual ellipses, which describe Conceptual ellipsoids that are generated by a combination of simple and complex sinusoidal oscillations with a diagonal that is a Natural Prime number. Again, when the force, "F," is a Natural integer, the Conceptual ellipsoid becomes a Pulsoid, which underlies the unimetry (geometry) of the first essence of mass.

Click below to See the:
Conceptual ellipse and Brunardot ellipse Tables:

Click Image for Larger View

There is one Universe.

It is perpetual, in equilibrium; and,

a manifestation of the . . . Unified Concept;

also,

Science, Theology, and Philosophy

are a single discipline, which proclaims the

perpetuity and nexus of Life; such is

. . . Conceptualism.

	the soliton, "s";
	the vector, "v"; and,
	the square of the Brunardot chord, "c."

	Light, "l";
	the perigee, "p";
	the radius, "r";