The Pythagorean Curvature Correction Theorem - a modified Pythagorean Thereom [View all]

Last edited Tue Feb 18, 2025, 01:44 PM - Edit history (7)

This idea is a simpler equation I've adapted from a new concept I call Pythagorean law. This is a modified version I call Pythagorean Curvature Correction Theorem. It's just a tool I use to approximate distances along a geodesic more easily and a lot more precisely. The equation is a little tough to understand as it produces multiple outputs that don't always make a lot of sense. I assure you, the imaginary results that you can get from this equation are very useful if you understand the conditions on which those values are derived.

There's a great deal about this new concept that is extremely complicated to explain so this is just intended as an introduction. I intend to put those further explanations in the new book I intend to publish in the very near future. Hope you enjoy the read. And don't forget to be very skeptical of any new math!
https://qmichaellewis.blogspot.com/2025/02/a-new-pythagorean-tool-for-curved-world.html

Beyond Flatland: Pythagorean Curvature Correction Theorem

For centuries, we’ve known the simple elegance of the Pythagorean theorem:

c² = a² + b²

This works perfectly in a flat world. But what happens when the surface isn’t a smooth plane—when it's curved, like the Earth or even spacetime itself?

That’s where a small but profound correction comes in:
Pythagorean Curvature Correction Theorem : c² = a² + b² + h (a²b² / R²)

h (a²b² / R²)
This extra term adjusts for curvature.

Breaking It Down Simply:
- a, b - > The two legs of a right triangle
- c - >The true shortest path (geodesic)
- R - >The curvature radius (e.g., Earth's radius)
- h - >The curvature type:
- h = -1 - >Spherical (Earth, planets)
- h = +1 - >Hyperbolic (saddle-shaped, deep space)

Why It Matters:
1. Globe Navigation: Flight paths follow curved geodesics, not straight lines. This correction gives accurate distances.
2. Cosmic Geometry: Galaxies exist in curved space—this helps measure their true separations.
3. Molecular Structures: Atoms don’t sit on a flat sheet—this refines molecular distances.
4. Wave Propagation: Signals and light waves move along curved paths—this helps track phase shifts correctly.

How to Use It:
1. Find your triangle’s sides a and b
2. Determine the curvature radius R
3. Select h (-1 for spheres, +1 for hyperbolic spaces)
4. Plug in the values and solve for c

Final Thought:
This isn’t just an abstract formula—it’s a practical tool for real-world applications, from air travel to quantum physics. The universe isn’t flat, and neither should our math be.


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If you're wondering if this is just a hack of the Unified Pythagorean Theorem, it is not. It is a complement to it. The Pythagorean Curvature Correction Theorem approximates the lengths of the sides more precisely and so the Unified Theorem can then approximate the area much more precisely. That's the idea, use them together and you have a very precise guess at a distance.

It's still not dead on balls accurate. There's still some terms you're missing in all of these theories but we won't delve into that at this point. Here is a blog post that describes each method and how to use them.

https://qmichaellewis.blogspot.com/2025/02/how-pythagorean-curvature-correction.html

The Unified Pythagorean Theorem by Dr. John Cook
https://www.johndcook.com/blog/2022/08/27/unified-pythagorean-theorem/