Understanding Syπ is the key to fully unlocking it’s extrapolation capabilities. I have known from the beginning that position Syπ(162) was the closest whole number which resulted in a number extremely close to the accepted value it pi. This value has a repeating decimal with a period of 3,961,920 digits.
We began to simplify Syπ with the goal of making it a single input function. As well as a means to understand it better and reduce the chance any possible errors.
We then simplified it even more.
Finally we substituted the actual values for 3 of the 4 initial inputs. Leaving only p (position) as the input.
This then further simplified to…
We simplified it one last time to arrive at the f(x) = a/(bx+c) form
This new form behaves exactly like the original Syπ Equation, specifically to the Syπ Gradient itself. It does not account for possible changes to the other 3 variables. It does provide great insight making it easier to understand and use in many ways.
As also noted we can calculate the (exact) position of Pi in the Gradient with the following formula.
This gives us an (exact) value that is exactly equal to the accepted value π, accurate to any desired number of decimal places. Show below matching the first 131 places.
Syπ(162.005531…) = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955
Pi = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955
This position function can be used to locate any approximation of PI.
As always you don’t have to take my word for it. Try it and see for yourself at my GeoGebra page https://www.geogebra.org/m/qsqgpqaw
You can check out the full model and see the connections to physics here https://www.geogebra.org/m/xrffzsng
Thank you. Stay Tuned.