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The Brunardot Theorem states that for all ellipses the diameter chord, “c,” squared equals twice the vector, “v,” squared minus the soliton, “s,” squared. [c² = 2v² – s²]

The Brunardot Theorem’s genesis is orthogonal dimensions, which are the genesis of the Pythagorean Theorem. [a² + b² = c²]

The Pulsoid Theorem states that for all ellipses the vector, “v,” equals the Elliptical Constant, “ε,” times the Pulse, “P,” squared. [v = εP²]

The Pulsoid Theory is the genesis of Einstein’s mass-energy equivalence formula. [E=mc²]

For all ellipses the Pulse, “P” is the distance from the elliptical center to a focus; and, the equivalent, peripheral distance from the end of the major diameter, “M,” to the nearest focus.

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For all ellipses the Key, “K,” is the radius, “Ko,” of a circle that is inscribed within a right triangle comprised of the focal length of an ellipse, which is referred to as the wave, “w,” and the two generating radii of the ellipse, which are referred to as the hypotenuse, “h,” and the radius, “r,” that together equal the major diameter, “M.” The right angle of the inscribing triangle is at a focus. [K = (r + w –h) / 2]

The inscribed circle is a heuristic representation of a three dimensional Resoloid.

The Resoloid is the genesis of mass; and, when ejected, the genesis of radiant energy . . . Light.

For all ellipses the Elliptical Constant, “ε,” which is the Pulse, “P,” minus the Key, “K,” equals One, “1.” [ε = P – K = 1]

It is the Elliptical Constant, “ε,” as expressed by the Pulsoid Theory that relates the values of every structural part of all ellipses to one another.

The Elliptical Constant, “ε,” is somewhat analogous to pi, “,” for the circle. A circle is a special ellipse with congruent foci. The Elliptical Constant, “ε,” is a more powerful constant than pi, “”; as, it is a difference rather than a ratio.

When the Pulse, “P,” is an integer, all salient elliptical components are always integers. Such an “integer” ellipse is referred to as a Brunardot Ellipse. See Appendix C: Legend.

The geometry of the ellipse, and its contained Elliptical Constant, “ε,” which equals One, “1,” is the genesis of the number system and most all mathematical logic; as well as, the invalidation of Kurt Gödel’s Incompleteness Theory concerning mathematical certitude.

A Pulsoid Ellipse is a Brunardot Ellipse with an integer obtuse amplitude, “ao”: and, an acute minor diameter, “Na,” that, with each pulse, rapidly converges to an integer When the value of the obtuse hypotenuse, “ho,” of a Brunardot Ellipse is continuously looped to the Pulse, “P,” recurring Pulsoid Ellipses are continuously generated.

The continuous generation of Pulsoid Ellipses is the genesis of fractal phenomena.

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