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

import math
import decimal


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


a1 = decimal.Decimal(1)
a2 = decimal.Decimal(2)
a3 = decimal.Decimal(3)
a4 = decimal.Decimal(4)
a5 = decimal.Decimal(5)
a7 = decimal.Decimal(7)
a79 = decimal.Decimal(79)

m1 = decimal.Decimal(-1)

x1 = a1/a7
x2 = a3/a79


# Reihenentwicklung für arctan(x)
k = 180

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 * (a5*t1 + a2*t2)
print(p)


print(((complex(7, 1)/complex(7, -1))**5)* ((complex(79, 3)/complex(79, -3))**2))