Ok, sometime ago I posted on Constructor’s Corner that a logarithmic spiral could be used to find a pattern in Prime numbers. And, I still believe so.
But first we should look at the patterns in series that are already described by a logarithmic spiral. Such series as Fibonacci series, logarithmic series are already series that the logarithmic spiral describes. We need to start with simpler series than something as puzzling as “a pattern in Prime numbers”.
On a recent comment to my YouTube video, a viewer commented that it has been proven that no polynomial equation describes Prime numbers. So my equation x^2+12.0958x-17.0219 could not describe Prime numbers. That is an equation of a parabola. However, I am not stating that the parabolic equation just mention is the pattern. Instead, I theorize that it is a parabola on which the Prime numbers that fall on it occur in a pattern. This pattern is what I am trying to use the logarithmic spiral to reveal the pattern.
My new interest is the slide rule. Slide rules use proportions to multiply and find values of logarithms. So if a logarithmic spiral did solve many types of series, instead of a complex computer program, the slide rule would easily compute, reveal, and solve many different types of series. That is something that they probably already do.
A video on YouTube showed how numbers corresponded along a straight line, once the values on the lines were spaced disproportionally, according to the series. It makes more since on the video at this link:
So in theory, I believe that a logarithmic spiral can explain many series. That is a logarithmic spiral or an approximate logarithmic spiral. By approximate logarithmic spiral I mean that the spiral is shifted by a function a distance from its original starting place.
The difficulty comes in finding such an equation that will describe the logarithmic spiral that describes the series. That is the logic behind starting with a simple series instead of the ultra-complex Prime number series. So even if we cannot find a pattern in Prime numbers, the theory may still be of some merit.
But until then...
May the Creative Force be with You
Hopefully it is clear what is being attempted to be solved here. I will post updates to better explain and hopefully solve this problem. This is a good group project. If you have read this and want to work on a problem email: firstname.lastname@example.org . Also more math can be found in the math_hunches section of Constructor’s Corner.