On a Proof π ≠ 3.14159... (Verifiable)

Beyond the boundaries of established science an avalanche of exotic ideas compete for our attention. Experts tell us that these ideas should not be permitted to take up the time of working scientists, and for the most part they are surely correct. But what about the gems in the rubble pile? By what ground-rules might we bring extraordinary new possibilities to light? If you have a personal favorite theory, that is in someway related to the Electric Universe, this is where it can be posted.
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A Gnostic Agnostic
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On a Proof π ≠ 3.14159... (Verifiable)

Unread post by A Gnostic Agnostic » Fri Dec 30, 2022 10:46 am

Since at least the time of Archimedes over 2000 years ago, mathematicians have been approximating the curvature constant. They've done this while/as assuming (without foundation) inscribed (n) & circumscribed (N) polygons of sides n=N indefinitely approaches the circumference of a circle with 0.000... margin of error. This assumption is over 2000 years old & has neither been proven nor challenged (until now.)

In light of the area of a circle being a = πr², two points:
i. Neither polygon ever has an area a equal to the circle they are approximating, and
ii. Neither polygon (therefore) has a radius equal (to the same.)
Conclusion: Archimedes' method is not a like-for-like comparison & is therefore invalid.

What's happening is: the circumscribed polygon is invoking an area greater than the circle while/as the inscribed is invoking less. This means the equivalent radii associated with each polygon are of a slightly larger & smaller circle(s)... not the one we want. If/as the areas are re-normalized, Archimedes' method only resolves up to a max. of 0.49952094... of a radius of 0.5000... which means 3.14159... is NOT the circumference of a circle whose radius is 0.5000... This also means the lower- and upper-bounds calculated using polygons are wrong: they wildly underestimate the actual radius.

As for proving & verifying π ≠ 3.14159...:
1. Plot two concentric circles x² + y² = 1/4 (minor) and x² + y² = 5/4 (major) to produce an annulus of area equation π((√5/2)² - (1/2)²) = π. Find its uniform width w = -1/2 + √5/2 & note this to be equal to the RECIPROCAL of the so-called "golden ratio".
2. Plot a point anywhere on the minor circle such as (0, 1/2) and square 3.14159...'s quarter off it via. (0, 1/2 + (3.14159.../4)²).
3. Find the square of the approximated pi's quarter catastrophically fails to satisfy the uniform width of the annulus.
For a formal proof, see https://papers.ssrn.com/sol3/papers.cfm ... id=4307169.

FAQ:
"Why should the square of 3.14159...'s quarter satisfy the width of this π annulus?"
If given a single r = 1/2 circle, if/as a second circle expands from inside it, each π/4 imperatively squares with itself at r = 1/2 & the result is the annulus whose width is imperatively the square of this length: (π/4)² = w = -1/2 + √5/2. By plotting the square of the approximated pi's quarter from the minor, we can try/test/falsify the numerical integrity of 3.14159... by showing there is not enough length in this number to satisfy the annulus. This is owing to Archimedes' crude approximation method & failure to challenge his assumptions re: an indefinite approach.

Any one quadrant sweep of length w = -1/2 + √5/2 contains the exact same area as the square of pi's quarter.
This implies a square-sweep equivalence wherein both produce and/or contain the exact same area.

"If π ≠ 3.14159... what does it equal?"
(π/4)² = w = -1/2 + √5/2
π/4 = √(-1/2 + √5/2)
π = 4√(-1/2 + √5/2)
= √(8√5-8)
≈ 3.144605511029693144...

This implies for p = 1/2 + √5/2 ≈ 1.618...
π = 4/√p
π² = 16/p
16 = pπ²
1 = p(π/4)²
wherein '1' is a product of the so-called golden ratio & square of pi's quarter.

One may also use an inverse square contained in a unit square/circle ratio 4r²/4ar² for r = 1/2:
(π/4)p = 4r²/4ar² = 1/a
p = 1/(π/4)²
p = 1/(π²/16)
p = 16/π²
π² = 16/p
π = 4/√p
etc.

There are many other ways, but the inverse square is irrefutable because the universe is based in/on it.
According to the inverse square law, the circumference of a circle whose radius is 0.5000... is NOT 3.14159...

How could everyone have had pi wrong for so long & how did nobody notice it?
1. Human ignorance (don't underestimate it - it is the underlying problem.)
2. Failure to challenge basic underlying assumptions (ie. lack of use of scientific method of falsification.)
3. Not a single mathematician has ever checked their approximation vs. reality.

In reality, a real 1000mm diameter circle certainly has a circumference of at least 3144.6mm (to within tolerance.)
The sooner humanity fixes this error, the better. If this error is not fixed, humanity is not going to accomplish anything beyond what it has.

danda
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Re: On a Proof π ≠ 3.14159... (Verifiable)

Unread post by danda » Fri Mar 03, 2023 5:39 am

Interesting insight, thx for sharing here.

I am not a mathemetician, but at first read it seems valid to me. fwiw.
How could everyone have had pi wrong for so long & how did nobody notice it?
1. Human ignorance (don't underestimate it - it is the underlying problem.)
2. Failure to challenge basic underlying assumptions (ie. lack of use of scientific method of falsification.)
3. Not a single mathematician has ever checked their approximation vs. reality.
This seems to be an ever recurring problem in science. I find it in every area I have studied. And what's worse is that many voices shout from the rooftops about the errors and just get ignored over and over. Teachers who believe wrong things teach that to students and on an on. It often amazes me that humanity has ever made any progress at all.
The sooner humanity fixes this error, the better. If this error is not fixed, humanity is not going to accomplish anything beyond what it has.
What do you see as the practical impact of this error/correction? ie, in what ways/areas may the error be limiting us, and in what ways might the correction help us advance?

Cargo
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Re: On a Proof π ≠ 3.14159... (Verifiable)

Unread post by Cargo » Sat Mar 04, 2023 6:30 am

Invaded by AI we are. How dandy danda.
interstellar filaments conducted electricity having currents as high as 10 thousand billion amperes
"You know not what. .. Perhaps you no longer trust your feelings,." Michael Clarage
"Charge separation prevents the collapse of stars." Wal Thornhill

danda
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Joined: Tue May 26, 2020 2:33 pm

Re: On a Proof π ≠ 3.14159... (Verifiable)

Unread post by danda » Sun Mar 05, 2023 10:03 am

Cargo wrote: Sat Mar 04, 2023 6:30 am Invaded by AI we are. How dandy danda.
what is your problem Cargo? Were you molested by an AI in your childhood or something?

I'm sorry to be crass, but this is the 2nd time you made this baseless AI accusation without provocation and I find it silly and tiresome.

Is this the new level of discussion here, claim that everyone else is an AI?

Roy
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Re: On a Proof π ≠ 3.14159... (Verifiable)

Unread post by Roy » Wed Nov 22, 2023 4:45 pm

Interesting. I thought pi is defined as the ratio (implying measuremnent) of the circumference of a Circle to its Diameter.
Pi = C / D. It has nothing to do with inscribed & circumscribed polygons, or algebraic series approximations that run on to a thousand decimal places beyond the means of accurate measurement.
It seems to me, one could take a milled coin, (say a copper, silver or gold ounce) mark one serration, and roll it on a piece of paper to mark out the circumference. Then, with suitable calipers, measure the diameter and marked circumference. Do the math, and you have the defined measure of Pi. Have a class of math students do this with different coins, analyze the results.
Probably close enough for government work.

I might do this experiment, if I can get a Round Tuit.

Lloyd
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Re: On a Proof π ≠ 3.14159... (Verifiable)

Unread post by Lloyd » Sat Nov 25, 2023 6:36 pm

Miles Mathis claims that Pi = 4 for equations involving motion, I guess because of momentum. Steve Ostdijk confirmed it with an experiment.

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