import matplotlib
import matplotlib.pyplot as plt
import numpy as np
from math import sqrt, inf
matplotlib.use('webagg')
matplotlib.use('qtagg')

def get_pi(n=2, should_plot=False):
    # x2 + y2 = 1
    xs = []
    ys = []
    qx = []
    qy = []
    ql = 0
    for x in range(0, 1001):
        x /= 1000
        y = np.power((1 - x**n), 1/n)
        if qx:
            ql += np.power((abs(x - qx[-1]))**n + (abs(y - qy[-1]))**n, 1/n)
        qx.append(x)
        qy.append(y)

    xs.extend(qx)
    ys.extend(qy)

    xs.extend(list(reversed(qx))[1:])
    ys.extend([y*-1 for y in reversed(qy)][1:])

    xs.extend([x*-1 for x in (qx)][1:])
    ys.extend([y*-1 for y in (qy)][1:])

    xs.extend([x*-1 for x in reversed(qx)][1:])
    ys.extend(list(reversed(qy))[1:])

    dia = ql*4
    pi = dia / 2

    if should_plot:
        plt.plot(xs, ys)
        plt.axis("equal")
        plt.show()

    return pi

print(1, get_pi(1, should_plot=True))
print(2, get_pi(2, should_plot=True))
print(3, get_pi(3, should_plot=True))
print(4, get_pi(4, should_plot=True))
print(5, get_pi(5, should_plot=True))
print(10, get_pi(10))
print(100, get_pi(100))
get_pi(99999999999999999999999999999999999999999999999, should_plot=True)

xs = []
ys = []
minpi = inf
minn = None
for n in range(1000, 10000):
    if n == 0:
        continue
    n /= 1000
    pi = get_pi(n)
    xs.append(n)
    ys.append(pi)
    if pi < minpi:
        minpi = pi
        minn = n

plt.plot(xs, ys)
plt.plot(minn, minpi, 'bs')
plt.show()