Discussion concerning the first major re-evaluation of Dewey B. Larson's Reciprocal System of theory, updated to include counterspace (Etheric spaces), projective geometry, and the non-local aspects of time/space.
Beyond Archimedes: A Pythagorean Theorem
Solution to Pi as Lone Unknown Triangle Side
Abstract. We explore the practical application of isoperimetric inequality (L² ≥ 4πA) to classical methods of circle measurement.
Exampling Archimedes' n-gon approach, we compare it to a real-world kinematic scenario of a unit diameter circle rolling on a flat plane surface.
Using annular geometry, we demonstrate that π can be derived algebraically by solving for the linear distance its centre travels per full revolution.
Unlike exhaustive methods involving non-circular figures, our annular approach begins with isoperimetric equality by deriving a right triangle
(with π its lone unknown side) & applying the Pythagorean theorem to it. This algebraic approach to π reveals unexpected yet significant connections
between it and the golden ratio. We further explore more assumptions underlying 3.14159... discovering its embedment in an unbounded plane to be
catastrophic & remedy with a bounded one. Finally, we close with a fresh new perspective on the notoriously unsolved Riemann Hypothesis problem.
Our result suggests both a need for physical experimentation, as well as a need to re-evaluate the general reliability of non-circular methods in rigorously
bounding and/or converging on the circle constant π.
This paper is academic in tone & presentation. If anyone is still around:
please check for errors, typos etc. and advise if improvements can be made.
Hi, i don't know if the 2.5k views of this post are all from google bot, but at least i am still around. Long time reader, never been a big poster. Dearly miss Bruce's insight, would love to see life coming back to this forum, so that his legacy could go on.
Your paper is very interresting but i'll have to go tru it a fourth and probably a fifth time before a can make any contructive comments on it.
Anyhow i encourage you to continue to post your ideas. I myself have some work/thought elaborated in the RS context through the years and i will try to find time to present them in a somewhat coherent manner.
Maybe with enough people's around we could manage to fill one of Bruce's shoe!
Alexis wrote: ↑Fri Aug 30, 2024 6:45 pmHi, i don't know if the 2.5k views of this post are all from google bot, but at least i am still around. Long time reader, never been a big poster. Dearly miss Bruce's insight, would love to see life coming back to this forum, so that his legacy could go on.
Hello,
Alexis wrote: ↑Fri Aug 30, 2024 6:45 pmYour paper is very interresting but i'll have to go tru it a fourth and probably a fifth time before a can make any contructive comments on it.
The paper conveys the Pythagorean theorem calculation of pi as being equal to 4√w ≈ 3.1446055... for w = √5/2 - 1/2, the inverse of the golden ratio.
It also addressed why 3.14159... is incorrect owing to a number of false assumptions made by Archimedes & mathematicians since.
The easiest way to understand this might be imagining Archimedes' n-gon method & realizing mathematicians do not account for the empty space outside the circle yet inside the square.
They are instead assuming an unbounded continuity of the plane... but pi is contained by a finite square with a finite space. In other words: pi is not "unbounded", it is bound
by the square of its own diameter. When mathematicians are assuming unbounded continuity, they are simply assuming more empty space outside the circle than actual.
Consequently, the area of the figure is being underestimated because the area outside the figure is being overestimated.
Alexis wrote: ↑Fri Aug 30, 2024 6:45 pm
Hi, i don't know if the 2.5k views of this post are all from google bot, but at least i am still around. Long time reader, never been a big poster. Dearly miss Bruce's insight, would love to see life coming back to this forum, so that his legacy could go on.
Your paper is very interresting but i'll have to go tru it a fourth and probably a fifth time before a can make any contructive comments on it.
Anyhow i encourage you to continue to post your ideas. I myself have some work/thought elaborated in the RS context through the years and i will try to find time to present them in a somewhat coherent manner.
Maybe with enough people's around we could manage to fill one of Bruce's shoe!
Hello again,
The previous response initially contained much more information, however it was censored by RSoT staff for allegedly containing so-called "personal attacks".
It was not directed at anyone personally therefore was not a personal anything, but that was the justification given to me. I am being threatened with a suspension too.
Accordingly, due to ongoing concerns with the direction RSoT has taken since Bruce's departure, I am no longer in support of the theory & this will be my last post here.
I therefore apologize I am not able to continue to post ideas or further insights, but RSoT staff has asked me to consider leaving & I agree it is best for all involved.
