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Inscribe Circles (incircles) FGJ and HIK with centers at and respective diameters LM and NO. Bisect Lines FG and HI with Center Lines. 
Construct a paired Pythagorean Triangle FGJ in accordance with base, side, and hypotenuse as indicated in the below Table of Formulas. A pair of Pythagorean Triangles have short sides, radius (r) and base (b), which vary by the Elliptical Constant (EC) = . 
Construct a Pythagorean Triangle
HIK in accordance with base, side, and hypotenuse as indicated in the below Table of Formulas. Pythagorean Triangles are triangles with a right angle; and, all sides that are integers. 
A Pythagorean Triangle Pair (PTP) can be mapped to every integer greater than One. Four angles (two of the six angles are right angles) and all six sides of a Pythagorean Triangle Pair are of unlike values. 
The simplest equation
for the indiameter of a circle inscribed within any right triangle is: 
An indiameter of a right
triangle equals side "a" plus side "b" minus the hypotenuse "c". 
Amazingly, the diameters of both circles inscribed within each different Pythagorean Triangle, of a given pair, are even integers, that are . . . identical to one another. Thus, the radii of the inscribed circles are also equal integers. 

One must
continuously ask: Why? Why? Why?; and, Why? again. And, realize that Fundamental Nature is the source of all Mathematics! 
Summary  Epsilon equals One  Proof of One  Inverse Square Law  Elliptical Constant 
revised Fibonacci Sequence 
Natural Function  Brunardot Theorem  Duality of Infinity  Challenge to Academe  Pulsoid Theorem  Fundamental Intrinsic Time 
Salient Structural Parts  Universal Locus  Heisenberg Uncertainty Principle  Heaven/God/Hell  Philogic  Entanglement 
Spin  Tini Circle Groups  Antimatter  Fabric of Space  Pauli Exclusion Principle  Table of Contents 