Monte Carlo · N=0

PERKIRAAN π

0.00000000

error: —

DI DALAM

TOTAL

LAJU PEMROSESAN

— iter/s

ALGORITME

π ≈ 4 × (inside / total)
inside  = Σ { x²+y² ≤ 1 }
x, y   ∈ [−1, 1]  (PRNG)
lim n→∞  ⟹  π

JEDA SETEL ULANG

Spiral Emas · φ

NILAI φ

1.61803399

(1 + √5) / 2

KONVERGENSI FIBONACCI

ALGORITME

φ  = lim F(n+1) / F(n)
F(n) = F(n-1) + F(n-2)
φ² = φ + 1
1/φ = φ − 1  ≈ 0.61803…
φ  = 1.6180339887…

JEDA SETEL ULANG

Lingkaran Satu · e^(it)

e^(iπ) + 1 = 0

Identitas Euler — Persamaan Paling Indah

angle t 0.000π

Re = cos(t) 1.0000

Im = sin(t) 0.0000

e^(it) = cos(t) + i·sin(t)
t = π  ⟹  cos(π) = −1
             sin(π) =  0
∴  e^(iπ) = −1
∴  e^(iπ) + 1 = 0  ■

∴ e^(iπ) + 1 = 0 ✓

QED

Π·φ Algorithm Lab

Π·φ LAB ALGORITME Π·φ