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.

(A Proof of One and the Unimetric Structure of Reality)

v = ep2 for
the ellipse: c2 = 2v2 - s2


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":

Light, "l";
the perigee, "p";
the radius, "r";
the soliton, "s";
the vector, "v"; and,
the square of the Brunardot chord, "c."

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:


There is one Universe.

It is perpetual, in equilibrium; and,

a manifestation of the . . . Unified Concept;


are a single discipline, which proclaims the

perpetuity and nexus of Life; such is

. . . Conceptualism.

Terms of: 
Copyright 1999-2007 by Brunardot

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