Editing Khinchin's constant (section)

==Open problems==
[[File:Geometric means of continued fractions to Khinchin constant.svg|thumb|The limits for <math>\sin1</math> (green), <math>e</math> (red), <math>\sqrt{31}</math> (blue) and a constructed number (yellow).]]
Many well known numbers, such as [[pi|{{pi}}]], the [[Euler–Mascheroni constant]] &gamma;, and Khinchin's constant itself, based on numerical evidence,<ref>{{Cite web|url=https://mathworld.wolfram.com/Euler-MascheroniConstantContinuedFraction.html|title=Euler-Mascheroni Constant Continued Fraction|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2020-03-23}}</ref><ref>{{Cite web|url=https://mathworld.wolfram.com/PiContinuedFraction.html|title=Pi Continued Fraction|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2020-03-23}}</ref><ref name=":0" /> are thought to be among the numbers for which the limit <math>\lim_{n \rightarrow \infty } \left( a_1 a_2 ... a_n \right) ^{1/n}</math> converges to Khinchin's constant. However, none of these limits have been rigorously established. In fact, it has not been proven for ''any'' real number, which was not specifically constructed for that exact purpose.<ref>{{Cite journal |last=Wieting |first=Thomas |date=2008 |title=A Khinchin Sequence |url=https://www.ams.org/journals/proc/2008-136-03/S0002-9939-07-09202-7/ |journal=Proceedings of the American Mathematical Society |language=en |volume=136 |issue=3 |pages=815–824 |doi=10.1090/S0002-9939-07-09202-7 |issn=0002-9939|doi-access=free }}</ref>

The algebraic properties of Khinchin's constant itself, e. g. whether it is a rational, [[Algebraic numbers|algebraic]] [[Irrational numbers|irrational]], or [[Transcendental numbers|transcendental]] number, are also not known.<ref name=":0" />