Ones that have periodic continued fractions are known as quadratic surds, and Rivoal proved that the form gamma of 2n+1 can generate infinitely many of them.
Hurwitz's Theorem gives the bounds for the best approximation to an arbitrary one of these. Ones that have periodic continued fractions are known as quadratic surds, and Rivoal proved that the form gamma of 2n+1 can generate infinitely many of them. Topologically, the set of them is a Baire space but is not locally compact. The Erdos-Borwein constant is this, as is Gelfond's constant, but this property is not known for pi to the e power or for the Euler-Mascheroni constant. FTP name these numbers that were feared by the Pythagoreans and that are non-terminating and non-repeating
Hurwitz's Theorem gives the bounds for the best approximation to an arbitrary one of these.
irrational numbers