Apa itu Konstanta Gelfond?

h1card_01p_02

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.

p_04

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

p_06links

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.

card_08card_09

Digunakan dalam

∑Matematika

✓

⚛Fisika

–

⚙Teknik

–

🧬Biologi

–

💻Ilmu Komputer

–

📊Statistika

–

📈Keuangan

–

🎨Seni

–

🏛Arsitektur

–

♪Musik

–

🔐Kriptografi

–

🌌Astronomi

–

⚗Kimia

–

🦉Filsafat

✓

🗺Geografi

–

🌿Ekologi

–

Want to test your knowledge?

Question

Apa masalah ke-7 Hilbert?

tap · space

1 / 10