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
. Its
square root
is
\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.
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