Khinchin's Constant

The almost-everywhere geometric mean of the terms in a real number's continued fraction expansion.

Specifications & Metrics

symbol

K

approx

2.68545200106430…

Core Principles & Analysis

• Khinchin proved in 1934 that for almost every real number the mean exists and equals it.
• No number has ever been proven to have this property — π and e are computed, not proved.
• Its value is known only by sampling random numbers and averaging their expansions.