Beyond Archimedes... (Paper, 18pp)

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.
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ckiit
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Joined: Sat Dec 21, 2019 7:54 am

Beyond Archimedes... (Paper, 18pp)

Post by ckiit »

Paper (.pdf, 18pp):

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.

https://vixra.org/pdf/2407.0150v1.pdf

Hard copy attached.
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Alexis
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Re: Beyond Archimedes... (Paper, 18pp)

Post by Alexis »

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! :)
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ckiit
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Re: Beyond Archimedes... (Paper, 18pp)

Post by ckiit »

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,

What follows is my own assessment of the events following Bruce's departure
keeping in mind I have no personal connection(s) to him, but am an outside observer.

One could say this is coming from the perspective of an "uncommitted investigator".

Bruce's departure fundamentally presented an important choice to be made: to move on, or not.
The lifelessness present is the natural consequence of the choice that was made to not.
Despite solving for unity & making the greatest discovery one could, RSoT chose not to move.

I may be told this isn't true after being cited all efforts to restore the sites & navigate legal matters.
However, I attended their recent webinar & left it knowing it is dead despite the previous.

There was & is no focus on the work done immediately following Bruce's death.
User737 & I did precisely what Bruce asked us to do: we kept moving forward.

Others did not. Unity has been solved for, for years now.

It was never about that, however.

I understand Bruce is sorely missed, but this is precisely why RSoT is dead.
Outstanding members were & are not in it for the sake of humanity, as Bruce was.

I tried to keep things moving forward after witnessing progress cease upon Bruce's death.
I did so successfully albeit for only a brief time through finding & conveying π ≠ 3.14159...
as being highly relevant to both the RSoT unity postulate & humanity as a whole.

This was picked up on by user737 who developed the insight beyond anything Bruce could have imagined.
However, other members ignored Bruce's request to keep working together & thereby ignored all work conducted by others.
As I write this, these members have yet to engage in any capacity whatsoever on the topic of pi & what it means for humanity.

Accordingly, I observe RSoT as succumb to an idolatrous worship of the late Bruce - not unlike any other religious cult.

I long ago accepted RSoT has decided the loss of a single life outweighs the loss of any & all others subsequent.
The nature of human ignorance is such that it motions in directions opposite to what is necessary to move on.
One would have hoped for a theory of a universe of motion to understand the need to move on, but here we are.

What was & is required to move on is moving on from Bruce.
Unfortunately, for only Bruce was it ever about humanity as a whole.
For his followers, it was just about Bruce. That's why RSoT is dead: Bruce is. It's that simple.

The followers will say "RSoT is not dead" and soon say "Bruce is not dead... he's here in spirit".
If Bruce were here in spirit, he would be thoroughly admonishing those who betrayed his request
because (perhaps) his restless spirit CAN see (& help "communicate") how important the work was/is.

This is only clear to those who have no a priori attachment(s) to the man Bruce:
all love for humanity RSoT ever had died with Bruce & so I now work alone.

Certain (but not all) members have effectively betrayed not only Bruce & his spirit, they betray all of humanity.
Ironically, they will believe the opposite given the extent to which they work to preserve anything & everything Bruce.
They chose to ignore any & all work done which was not by Bruce even as strictly contrary to Bruce's wishes.

Accordingly, RSoT is dead on matters of principle: Bruce's wish was betrayed
& in its place is a scramble to compile & preserve anything & everything Bruce
while trying to preserve a legacy of Bruce. It was never about unity... only about Bruce.

RSoT was & is a cult of Bruce. The sooner one can see this, the better off one will be.
Those who did what Bruce asked produced what Bruce wanted, but others ignored it
& continue to because they couldn't care less about anyone or anything but Bruce.
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 pmAnyhow 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! :)
Bruce specifically asked everyone to continue to work together, but some chose to ignore this wish.
Instead, they ignored the work done by others despite how significant it was & continues to be.
It is ironic (albeit not surprising) those closest to him would be the same to betray his wish.

The problem I observe is none of his followers care about the state of humanity the way he & even Larson did. The others here were & are
only here for Bruce's sake... without so much as sharing in Bruce's larger concern for humanity. Accordingly, I do not work around here anymore
because the concern for humanity Bruce had died with Bruce & is no longer present in RSoT as a primary motivation for further research.

My primary motivation for research has been out of concern for the problem of human suffering.
I sought Bruce's insight on a theory of it because I recognized he had a genuine concern for humanity.
I wasn't able to present the theory before he died, but I have been around long enough to know this:
there is nobody left at RSoT seeing a bigger picture beyond Bruce because he was their bigger picture.

The actual bigger picture was & is in the correction to pi, but because it didn't come from Bruce... it went ignored.
I therefore accept the demise of RSoT because it is the natural consequence of the human ignorance underlying it.

RSoT was described by Miles Mathis as a cult. I agree with this assessment: it is a cult of Bruce.
As a consequence of this, the most important work conducted since his death has gone ignored.
This continues to be true because those closest to him share not in his love for all of humanity
but instead betray his spirit by doing the exact opposite of what he actually asked for:
they refuse to work with others & their ideas. Do not be surprised if you find this true
should you post your own contributions & witness no interest. Just don't take it personally:
these people are in a cult & they actually do not care about humanity at all like Bruce did.
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