Gelfond–Schneider constant

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The Gelfond–Schneider constant is

<math>2^{\sqrt{2}}=2.6651441...</math>

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.

Its square root is

<math>\sqrt{2}^{\sqrt{2}}=1.6325269...</math>

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.

See also

Gelfond's constant