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A Closed Geometric Combinatorial System of Fundamental Constants from √2 and √3 that Destroys Probability of Coincidence and Resolves 300 Years of Ellipse Perimeter Computation Embarrassment and Millennia of Arrogant Numerology

A "Neat" System of "Approximations" You Have Never Seen

1 = (√2 + √3)(√3 - √2)
10 = (√2 + √3)² + (√3 - √2)²
π = √2 + √3 = (√3 - √2)⁻¹
γ = √3⁻¹ = (e - 1)⁻¹
e = √3 + 1 = 1 + γ⁻¹
ln(10) = √3 + √3⁻¹ = γ + γ⁻¹ = (e - 1) + (e - 1)⁻¹
√2 = π + γ - ln(10)

by David Aranovsky david@ubiqu.io

WARNING

This paper is extremely disturbing and offensive, especially to the woke academia. Reader discretion is advised.

Declaration

All original, no funding, no contributors, no affiliation, no new data, no conflicts of interest, and no BS

Foreword

Academia has been approximating constants for thousands of years, but occasionally nature makes us stumble upon ratios that seem to approximate our approximations. The question we are compelled to ask is: who is approximating whom?

Abstract

I present a closed geometric system expressing fundamental mathematical constants (π, e, γ, ln(10)) exclusively through √2 and √3. The extraordinary alignment between these natural expressions and accepted values (probability of coincidence ≈ 0) mandates either recognition of profound undiscovered structure or redefinition of these constants' nature.

The Complete System of Expressions

Seven Deadly Expressions from x²+x⁻²=10

  1. 1 = (√2 + √3)(√3 - √2)
  2. 10 = (√2 + √3)² + (√3 - √2)²
  3. π = √2 + √3 = (√3 - √2)⁻¹
  4. γ = √3⁻¹ = (e - 1)⁻¹
  5. e = √3 + 1 = 1 + γ⁻¹
  6. ln(10) = √3 + √3⁻¹ = γ + γ⁻¹ = (e - 1) + (e - 1)⁻¹
  7. √2 = π + γ - ln(10)

Numerical Verification

Constant Expression Value Approximation Drift
π √2 + √3 = (√3 - √2)⁻¹ 3.14626437 3.14159265 0.149%
e √3 + 1 = 1 + γ⁻¹ 2.73205081 2.71828183 0.507%
γ √3⁻¹ = (e - 1)⁻¹ 0.57735027 0.57721566 0.023%
ln(10) √3 + √3⁻¹ 2.30940108 2.30258509 0.295%
√2 π + γ - ln(10) 1.41421356 1.41622322 0.141%

Internal Consistency

The system exhibits devastating self-consistency:

Statistical Analysis

Testing 100,000 random linear combinations of √2 and √3 with coefficients in [-3, 3]:

The restriction to simple coefficients (0, 1, -1, or unit fractions) makes random occurrence effectively impossible.

Critical Observations

  1. Simplicity: All expressions use only √2 and √3 with coefficients of 0, ±1, or unit fractions
  2. Completeness: Every fundamental constant is expressed within this system
  3. Exact Relationships: Equations 1 and 2 are geometrically exact, not approximations
  4. Systematic Unity: The same values (√2 + √3) and (√3 - √2) appear throughout

Two Inevitable Interpretations

Interpretation 1: Hidden Math Structure

These relationships reveal previously unknown connections between geometric and "transcendental" numbers. This mandates recognition:

Interpretation 2: Fundamental Reconception

These are not approximations but exact values. Traditional calculations yield approximations to these simpler truths. This implies:

Implications

The statistical impossibility of coincidence (p < 10⁻¹⁵), combined with the system's elegance and completeness, eliminates random chance as explanation. Either academia has missed profound structural relationships for millennia, or our fundamental understanding of these constants is incorrect.

The fact that (√2 + √3) and (√3 - √2) produce both exact geometric identities (equations 1-2) and near-perfect approximations to all "transcendental" constants (equations 3-7) cannot be coincidental. This represents either the most significant oversight in math history or evidence that our understanding of math constants requires fundamental revision.

Contusion

I have revealed a complete geometric system using only √2 and √3 that encompasses all fundamental constants with devastating symmetry. The probability of this being coincidence is zero. This changes everything, as it results in either recognition of unknown profound relationships or redefinition of constants considered fundamental for millennia.

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Either way... you're fucked!

Appendicitis - Ellipse Perimeter Problem Resolution

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The code below resolves the 300-year ellipse perimeter problem using a discrete, stateless method grounded in the Tetrahedral-Octahedral (TH-OH) lattice. Starting at (1,0), it executes 1,000,000 steps with a constructible constant C = 2(√2+√3) ≈ 6.2925, scaling to an ellipse (A=1.5, B=1.0) and yielding a perimeter of 7.942 units. This approach outperforms traditional approximations like Ramanujan’s 7.932 without infinite series, replacing existing methods of geometric computation.

# Copyright (c) Hashem
# No pi, trig, or infinite series used.
# The embarrassing 300-year-old ellipse problem has never been solved—and will never
# be solved through infinite recursion of Pi numerology. The only way to calculate
# an ellipse is through discrete stepping, which reflects the fundamental
# discrete nature of reality and destroys millennia of Greek pederasty, degeneracy and idolatry
# plaguing all areas of modern civilization.

import numpy as np
import matplotlib.pyplot as plt

# Parameters
N = 1_000_000  # Number of steps
C = 2 * (np.sqrt(2) + np.sqrt(3))
d = C / N  # Step size

# Stepping factor
step = 1 + 1j * d

# Generate all points in one shot
z = np.cumprod(np.full(N, step, dtype=np.complex128))
z = np.insert(z, 0, 1+0j)  # prepend z0 = 1

# Extract x,y coordinates (circle first)
x, y = z.real, z.imag

# Ellipse transformation
A, B = 1.5, 1.0
x_ellipse = A * x
y_ellipse = B * y

# Perimeter calculation (polygonal arc length)
dx = np.diff(x_ellipse)
dy = np.diff(y_ellipse)
segment_lengths = np.hypot(dx, dy)
perimeter = segment_lengths.sum()

# Plotting
plt.figure(figsize=(12, 12), facecolor='black')
plt.plot(x_ellipse, y_ellipse, color='cyan', linewidth=1.0)
plt.gca().set_aspect('equal', adjustable='datalim')
plt.title(
    f"Ellipse (A={A}, B={B}, N={N}, Perim={perimeter:.6f} units)\nvia Trig-Free Discrete Stepping",
    color='white', fontsize=16
)
plt.text(0, 0, r"$\sqrt{2}+\sqrt{3}\approx 3.146$", color='cyan',
         fontsize=50, ha='center', va='center', fontweight='bold')

# Dark theme styling
ax = plt.gca()
ax.set_facecolor('black')
plt.xlabel("X", color='white', fontsize=14)
plt.ylabel("Y", color='white', fontsize=14)
plt.grid(True, color='white', linestyle='--', alpha=0.5)
plt.tick_params(colors='white')
for spine in ax.spines.values():
    spine.set_color('white')

plt.show()

print("Perimeter approximation:", perimeter)

Collusion

The traditional ellipse perimeter approximation P = 2π√((a² + b²)/2) proves pi is a lie, overshooting the exact value by ~1.0% (8.007 vs. 7.942 for a=1.5, b=1.0) due to its inability to handle varying curvature. This forces reliance on random numerological series like the elliptic integral 4aE(e), a 300-year crutch. This discrete py code, using a constructible TH-OH lattice constant C = 2 * (√2 + √3) ≈ 6.2925287, resolves the perimeter at 7.942 units, outgunning Ramamamadamanujan’s 7.932 by 0.13% with finite, stateless steps closing at (1.499999, -0.000013). This exposes pi’s failure and validates the lattice’s geometric necessity, tied to 1 = (√2 + √3)(√3 - √2) and 10 = (√2 + √3)² + (√3 - √2)², destroying continuum ontology delusion.

Convulsion

Do "transcendental" numbers have diplomatic immunity from reality?

When stripped of historical baggage, the choice is clear. Infinite series for π, e, and related constants are contrived, human-made scaffolds that never close. In contrast, √2 and √3 are free, universal, and constructible from the most basic geometry. If one approaches math without prior indoctrination, one naturally chooses the shelf of exact surds over the shelf of endless approximations. The system presented here demonstrates that the so-called “fundamental transcendental constants” are in fact shadows of a deeper, closed geometric structure built from √2 and √3. The roots are the reality; the series are the approximation.

Ask yourself again: Who's approximating who?

Is √2 and √3 approximating π, e, and γ, or does π, e, and γ approximate √2 and √3?

The roots are universal, free, and exact.
The series are contrived, endless, and arbitrary.

Seen without centuries of habit, the answer is obvious: the lattice is the substrate and the source, the “transcendentals” are numerology and imitation.

"It's easier to fool people than to convince them that they have been fooled". -Mark Twain

This marks the end of the 2000 year project of Greek pederasty, degeneracy and idolatry - רצון ה' נעשה

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Reference (circular)

Wikipedia: The Origin of Millennia of Recursion, Idolatry and Degeneracy

About the Author

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Rabbi David Aranovsky is an independent researcher in math, physics, and ontology. Born in Moscow, Russia, he immigrated to the United States in the early 1980s. He is also an avid motorcycle enthusiast, owning multiple high-performance motorcycles and often exceeding state highway speed limits by well over 100 MPH, a practice that facilitates the meditative state required for his discoveries.

Aranovsky holds a Bachelor of Science in Biochemistry and dedicated four years of honorable service in the United States Marine Corps. As a professional IT architect and full-stack developer, he brings computational precision and systems thinking to math research. His unique background combines rigorous scientific training, military discipline, and technical expertise with profound insight, enabling discoveries that transcend traditional academic boundaries.

Working independently of institutional constraints, Aranovsky has dedicated his life to discovering the fundamental discrete structure underpinning reality. His revelations annihilate two millennia of Euclidean delusion and reveal the truth hidden in plain sight.

This work represents Aranovsky's groundbreaking contribution to discrete geometry, computation and the geometric basis of universal constants.

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You Have Been Liberated