**Brunardot Triangles (BTr)**

The term "Brunardot Triangle" refers to a pair of primitive Pythagorean triangles each with a side that differs by the Elliptical Constant (EC); One.

Brunardot Triangles are extremely important for describing the relationship between protons, electrons, and neutrons within atoms and "dark" matter.

Brunardot Triangles are unending sequences of paired primitive Pythagorean triangles (each similar to a Pythagorean triangle, a² + b² = c², with all sides as integers) in which each triangle of the pair (of every sequence) can be

**mapped to the same Natural integer that can be**

*any*Natural integer.(If no image appears below,

*"Click"*your browser "Refresh" icon.)One of the paired Brunardot Triangles has a hypotenuse, “h,” that is equal to the base, “b,” plus one;

such as: 3-4-5 and 5-12-13 triangles. (h = b + 1)

The other paired Brunardot Triangle has a hypotenuse, “H” that is equal to the base, “B,” plus two;

such as: 8-15-17 and 10-24-26 triangles. (H = B + 2)

If the radius of the inscribed circle,“x”, is any Natural integer than the sides of the paired, primitive Pythagorean triangles are:

**a = 2x + 1**

b = (a² – 1)/2

h = b + 1

b = (a² – 1)/2

h = b + 1

A = a + 1

B = (A/2)² – 1

H = B + 2

A = a + 1

B = (A/2)² – 1

H = B + 2

the relationships apply to subatomic particles and their complex, oscillating, force fields.

**triangle of the Brunardot Triangle pair.**

*each***Radius of inscribed Pythagorean circle**

**x = (a + b – h)/2 = (A + B –H)/2.**

All Brunardot Triangle pairs generate an acute and an obtuse Brunardot Ellipse (BE) that each has a radius, “r,” equal to the altitude, “a,” (short leg) of its respective Brunardot Triangle. (Thus, it is possible to relate the symbolic Brunardot Triangle hypotenuses to the natural Emergent Ellipsoid hypotenuses (EEd), or fundamental quantum.

**Examples of Brunardot Triangles**

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