Open Problems
- Among the numbers whose geometric mean of the coefficients ai in the continued fraction expansion apparently (based on numerical evidence) tends to Khinchin's constant are π, the Euler–Mascheroni constant γ, and Khinchin's constant itself. However, none of these limits has been rigorously established, even though it is known that almost all real numbers have this property.
- It is not known if Khinchin's constant is a rational, algebraic irrational or transcendental number.
Read more about this topic: Khinchin's Constant
Famous quotes containing the words open and/or problems:
“What I mean by the Muse is that unimpeded clearness of the intuitive powers, which a perfectly truthful adherence to every admonition of the higher instincts would bring to a finely organized human being.... Should these faculties have free play, I believe they will open new, deeper and purer sources of joyous inspiration than have yet refreshed the earth.”
—Margaret Fuller (1810–1850)
“I had many problems in my conduct of the office being contrasted with President Kennedy’s conduct in the office, with my manner of dealing with things and his manner, with my accent and his accent, with my background and his background. He was a great public hero, and anything I did that someone didn’t approve of, they would always feel that President Kennedy wouldn’t have done that.”
—Lyndon Baines Johnson (1908–1973)