Apa itu Konstanta Gelfond?

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Gelfond's constant near 23

e^π sits tantalizingly close to 23 but misses by 0.14. The coincidence e^π - π ≈ 19.999 is even closer but equally meaningless.

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What the Gelfond-Schneider theorem proves transcendental

Table showing examples of numbers proved transcendental by Gelfond-Schneider

Ausdruck	a	b	Ergebnis
e^π = (-1)^(-i)	-1	-i	transzendent
2^√2 (Hilbert)	2	√2	transzendent
√2^√2	√2	√2	transzendent

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e^π vs π^e: which is larger?

e^π > π^e. This can be proved without a calculator: the function x^(1/x) has a maximum at x=e, so e^(1/e) > π^(1/π), which gives e^π > π^e.

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