Riemann was one of the finest pure mathematicians of his century.  ...within his mind burned the desire to understand the nature of the physical world...

Anticipating relativity and modern cosmology, Riemann understood that in order to grasp the meaning of the physical world, one had to develop a deep understanding of...geometry.

Amir D. Aczel [circa 1953- ]
    -God's Equation, 1999

 The general theory of relativity splendidly justified his (Riemann's) work.

In the mathematical apparatus developed from Riemann's address, Einstein found the frame to fit his physical ideas, his cosmology, and cosmogony: and the spirit of Riemann's address was just what physics needed: the metric structure determined by data.

Hans Freudenthal [1905-1990]
   -Dictionary of Scientific Biography, 1970-90
Seminal motion manifests as an elliptical pulse, which is described by the Brunardot Series.

The Brunardot  Series is unique in that it defines ellipses, which determine the Conceptual Unit . . ."One," 1, which is referred to as "the Proof of One."

The Brunardot Series, additionally, locks together Phi, F, the Golden Ratio, and the Fibonacci series, while completing said Fibonacci series by disclosing two additional terms.


Unimetry describes

 the Natural creation of mathematics

that begins with Brunardot ellipses,

which are two-dimensional, heuristic,

manifestations of a seminal pulse.
   

Brunardot Ellipse

("Click" the Image for a larger view.)

 


The Pulser of any ellipse is:

the three defining structural parts

 that are in the order of an additive series.

The structural parts are: perigee, p; soliton, s; and vector, v;

(p + s = v).

 The Pulser for all Brunardot ellipses are:

the first three terms of a Brunardot Series.

 


 The Brunardot Series are unending series,

 of unending terms,

that have a Natural integer for the second term and

the third term is the square of the first term and,

as with successive terms,

the sum of the preceding two terms.

 


There are several forms of Brunardot ellipses.

Four such forms are:

Seminal ellipses, Natural ellipses,

Conceptual ellipses, and Harmonic ellipses.

Seminal ellipses are Brunardot ellipses, which have have

the soliton, s, and the diagonal, d,

as Natural integers.  Natural ellipses are Seminal ellipses

when the perigee, p; the vector, v; and, the radius. r,

are Natural Integers.  Conceptual elipses are

Natural ellipses when the force, f, is a Natural integer.

Harmonic ellipses are Conceptual ellipses,

which have the radius, r, as a square. 

 

Summery: The value of any term of the pulser defines a Brunardot ellipse.

 

 

 

 

 

 

 


Fibonacci ellipses are are any ellipse where

the Pulser and apogee, a,

are terms of an additive series in the manner of a

generalized Fibonacci series.

 


The Brunardot Theorem, which applies to

all Fibonacci ellipses, states that:

c2 = 2v2 - s2

where: c = a major chord of the ellipse.