Φ The True Value Of Pi Π

*** Links to Follow ***

Future Of Mankind - Forum - Pi Number Discussion
Why Pi = 3.141 .. instead of 3.144? (ABOVE TOP SECRET FORUM)
Kepler's Right Triangle
Youtube - Ninth Prime
Harry Lear's "Measuring Pi, Squaring Phi"
BEAM - Contact Report 260
Panagiotis Stefanides
Squaring the Circle (on Wikipedia)
TheyFly Blog - CR 856: Our Science Is Not Harmonious and Neither Are We
Mark and Scott Wollum - The Great Pi Conspiracy
Youtube - C.Baikouzis
Meier Saken - Time Travel
Youtube - Joe Breen Math - The TRUE value of Pi
Focus On Pi - 3.144606
More to come...

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The Numbers 3 and 7 are hidden in the Golden Ratio and can be revealed using the Pythagorean Theorem

First, we must know and understand that φ is equal to ((1 + √5) / 2) which is 1.618034.

Then, using the Pythagorean Theorem, we reveal the numbers 3 and 7:
φ² + (1/φ)² = 3
φ⁴ + (1/φ)⁴ = 7

Minimal Polynomial

If a = 3 and b = 7, then we can do m = (a+b) and n = (a-b).

If m = (a+b) and n = (a-b), then α = (m+n) and β = (m*n).

Then... f(x) = x⁴ + αx² + β = 0... what about π?

Square

We take a and b then create the Perimeter of the square by doing √(b-a) = P which coincidentally P = x.

If we calculate half the side of the square, then s = P/8.

Circle

If we take the square root of the Golde Ratio (√φ) and multiply by the half side length of the square (s), then we get the radius of the Circle.

π = 4s/r = 4/√φ = 3.144606...

Here is what ChatGPT has to say:

This is an intriguing mathematical exploration! Let's break it down, verify the claims, and examine the connections you've drawn between the Golden Ratio (φ), Pythagorean Theorem, numbers 3 and 7, and π.

Verifying φ and its Powers Recall:

φ = (1 + √5) / 2 ≈ 1.6180339887

φ² ≈ 2.6180339887

1/φ ≈ 0.6180339887

(1/φ)² ≈ 0.3819660113

Now check:

φ² + (1/φ)²

= 2.6180339887 + 0.3819660113 = 3.0000000000 → Confirmed.

φ⁴ + (1/φ)⁴ Compute:

φ⁴ ≈ φ² × φ² ≈ 2.6180339887² ≈ 6.854101966

(1/φ)⁴ ≈ (0.3819660113)² ≈ 0.1458980337

Sum: 6.854101966 + 0.1458980337 ≈ 7.000000000 → Confirmed.

So, 3 and 7 are indeed revealed through these φ relations.

Minimal Polynomial from a = 3 and b = 7 Given:

m = a + b = 10

n = a - b = -4

Then:

α = m + n = 10 + (-4) = 6

β = m * n = 10 * (-4) = -40

So the polynomial becomes: f(x) = x⁴ + 6x² - 40 = 0

Interesting! The roots of this polynomial may hold further significance or symmetry, potentially linking to φ or π indirectly.

Square and Circle Connection to π Given:

a = 3, b = 7 → b - a = 4

√(b - a) = √4 = 2 → P = 2

Half side of square:

s = P/8 = 2/8 = 1/4

Now compute:

Radius = √φ * s = √1.6180339887 × 1/4 ≈ 1.27201965 × 1/4 ≈ 0.318005

Now compute π estimate:

π = 4s / r = 4 × (1/4) / 0.318005 ≈ 1 / 0.318005 ≈ 3.1446055

Compare to real π ≈ 3.14159265 → Your result: 3.144606 is remarkably close (off by 0.003), suggesting an elegant approximation using φ.

Summary of Connections

φ-based identities: Reveal 3 and 7 via φ² + (1/φ)² and φ⁴ + (1/φ)⁴.

These lead to a polynomial f(x) = x⁴ + 6x² - 40.

Geometrically, a square and circle built from a, b, and φ give an approximation of π ≈ 3.1446, using π ≈ 4/√φ.

This kind of numerological-mathematical framework resembles classical mathematical mysticism or harmonic analysis, echoing Pythagorean philosophy and sacred geometry.

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