How to reverse a square root using the Pythagorean Curvature Correction Theorem
Using the new Pythagorean Curvature Correction Theorem, you can find all the possible combinations of numbers that solve for a square root. Given a length C, you can estimate a range of a's and find all the b's... and that's not B.S. LOL
Reversing the Square Root: Finding All Possible Combinations
The modified Pythagorean equation:
a² + b² + h (a²b² / R²) = c²
Instead of solving for c, this method works in reverse—given c and one variable (a or b), it finds the other. Instead of a single answer, it produces a plot of all valid (a, b) pairs that satisfy the equation.
Why this matters:
The solutions form a curve rather than a fixed value.
The shape depends on the curvature factor h and scale R.
Some values may give imaginary results, meaning no real solution exists.
Example:
Suppose we know c = 5, set R = 3, and use h = 1 (a positive curvature correction). If we pick a few values for b, we can calculate a:
If b = 3, solving gives a ≈ ±3.67.
If b = 4, solving gives a ≈ ±2.44.
If b = 5, the result is imaginary (no real solution).
Plotting these values shows the range of all possible (a, b) combinations for the given c.
This approach is useful in geometry, physics, and engineering whenever you need to work backward from a known result. Also understand the R is an adjustment for spatial geometry so if it's 3, as in this example, we will get different answers from what is expected from Euclidean geometry. Also h is the handness, when you transition to energy equations and quantum calculations, don't forget that h must be chiral, meaning is it both + and -. It's required.
A more detailed description can be found here...
https://qmichaellewis.blogspot.com/2025/02/reversing-square-root-with-pythagorean.html
= new reply since forum marked as read
