python pi 圓周率 機率 驗證

points = 10000

X = np.random.uniform(-1, 1, points)

Y = np.random.uniform(-1, 1, points)

# 落於圓內的點

inner_index = (X**2 + Y**2) <= 1

# 落於圓外的點

outer_index = ~inner_index

indices = (inner_index, outer_index)

X_inner, Y_inner = X[indices[0]], Y[indices[0]]

X_outer, Y_outer = X[indices[1]], Y[indices[1]]

[(X_inner, Y_inner), (X_outer, Y_outer)], indices

plt.scatter(X_inner, Y_inner,s=1,c='red',marker='o',alpha=0.8,label='C1')

plt.scatter(X_outer, Y_outer,s=1,c='blue',marker='o',alpha=0.8,label='C1')

plt.show()

percent = len(X_inner) / points

print("圈內機率:",percent)

print("圈內面積:",2 * 2 * percent)

print("實際pi:",np.pi)

print("gap:",np.pi - 4 * percent)