(6-30-21): Every Right Triangle also has an entangled ‘LEFT’ or (inverse much smaller fractal) Triangle with identical proportions and inner angles, but non-reciprocal Base Values. For example, for any given Right Triangle, the Height x Hypotenuse defines the difference in size of its Left (reciprocal) counterpart. In a 3:4:5 Right Triangle (swipe right for 3-4-5 analysis) it’s dimensions are as follows, (LT: 3-4-5: .15-.2-.25 = 1/5 and 1/4 for its Height and Hypotenuse). See images for its corresponding Area, Perimeter, Inradius and Circumradius values.
The scaling difference is the Perimeter value. Perimeter (RT) / Perimeter (LT) = 12 / .6 = 20. And Height (4) x Hypotenuse (5) = 20. This is acting as an inverse Logarithm (which is NOT simply an inverse Log or exponent). Rather it is a multiplication of the Height and Hypotenuse instead of a ratio of the two (division) which division does define the Log and Exponential Base. The Left Triangle carries the characteristics of the Right Triangle with identical proportional measurements of θ° (and therefore β° also). For example note the 3 Base value for the Right Triangle. It’s ‘sister’ Left counterpart value Base is therefore 3/20 or .15. Like the Perimeter differential which is determined by Height x Hypotenuse, the numerator of the Left Triangle’s Base value is the same value as the Right Triangle’s Base Value (3). It’s denominator is simply the product of Height x Hypotenuse of the Right Triangle (and the product of the denominators of the Height and Hypotenuse of the Left Triangle 1/5 and 1/4 = 20. Therefore 3/20 or .15.
There appear to be many other new inverse and complementary relationships between Pythagorean functions of Right and Left Triangles. The above functions and relationship appear to apply to EVERY possible Right and Left Triangle pairing. I encourage everyone to find this one their own and test it out, it works every time. This also leads to more questions about the impact on Elliptic Curve and discreet logarithms…..