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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. 
x  =  Integer (base 10)=b/2 
Table of Formulas 
Pythagorean Triangle 
HIK  =  Pythagorean Vector Triangle 
HI  =  base (b), Vwave, (Vw)  =  2x 
HK  =  Vradius (Vr)=b^{2}/4 –  =  x^{2}– 
IK  =  Vhypotenuse (Vh)=b^{2}/4+  =  x^{2}+ 
The Pythagorean Theorem, a2 + b2 = c2, is an an incredible coincidence of number theory, which arises from the Emergent Ellipsoid and the Natural source of Mathematics. 

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  Duality of Infinity 
Natural Function  Brunardot Theorem 
revised Fibonacci Sequence 
Challenge to Academe  Pulsoid Theorem  Fundamental Intrinsic Time 
Salient Structural Parts  Universal Locus  Antimatter  Heaven/God/Hell  Philogic  Entanglement 