Khinchin's Constant Explorer

Universal limit of continued fraction geometric means $K_0 \approx 2.685452$

K₀ Benchmark: 2.685452

Preset Name Pi (π)

Terms Expanded 15

Running Geom Mean 2.6833

K₀ Absolute Delta 0.0022

Active Convergent 355/113

Number Decomposition Continued Fraction

Preset

Max Terms 15

Term: 15 / 15

Brackets Notation [a₀; a₁, a₂, ...]

Convergents (pₖ / qₖ)

Geometric Mean Trajectory vs Khinchin's K₀ Target K₀ = 2.685452

Gauss-Kuzmin Term Frequency Comparison P(aₖ = k) = -log₂ (1 - 1/(k+1)²)