Gelfond-Schneider constant

The Gelfond-Schneider constant is

$2^\sqrt{2}=2.6651441...$

which Aleksandr Gelfond proved to be a transcendental number using the Gelfond-Schneider theorem , answering one of the questions raised in Hilbert's seventh problem.

$\sqrt{2}^\sqrt{2}=1.6325269...$

which can be used in a nonconstructive proof that an irrational number to the power of an irrational number can sometimes produce a rational number.

Last updated: 08-21-2005 05:20:14

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