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:
“Agnosticism is a perfectly respectable and tenable philosophical position; it is not dogmatic and makes no pronouncements about the ultimate truths of the universe. It remains open to evidence and persuasion; lacking faith, it nevertheless does not deride faith. Atheism, on the other hand, is as unyielding and dogmatic about religious belief as true believers are about heathens. It tries to use reason to demolish a structure that is not built upon reason.”
—Sydney J. Harris (1917–1986)
“Imagination is a valuable asset in business and she has a sister, Understanding, who also serves. Together they make a splendid team and business problems dissolve and the impossible is accomplished by their ministrations.... Imagination concerning the world’s wants and the individual’s needs should be the Alpha and Omega of self-education.”
—Alice Foote MacDougall (1867–1945)