"""
Berechnung von pi über arctan(x)
(c) Jürgen Meier
www.3d-meier.de
24.06.2024
"""

import cmath
import decimal


# Anzahl Kommastellen
decimal.getcontext().prec = 105


a1 = decimal.Decimal(1)
a2 = decimal.Decimal(2)
a4 = decimal.Decimal(4)
a7 = decimal.Decimal(7)

m1 = decimal.Decimal(-1)

x1 = a1/a2
x2 = a1/a7


# Reihenentwicklung für arctan(x)
k = 300

t1 = 0
for n in range(0, k + 1):
    a = (((m1)**n)*(x1**(a2*n + a1)))/(a2*n + a1)
    t1 = t1 + a

t2 = 0
for n in range(0, k + 1):
    a = (((m1)**n)*(x2**(a2*n + a1)))/(a2*n + a1)
    t2 = t2 + a

p = a4 * (a2*t1 - t2)
print(p)

print(((complex(2, 1)/complex(2, -1))**2)* ((complex(7, 1)/complex(7, -1))**-1))