import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

# 圆的半径
radius = 1.0
init_n = 6
max_frame = 10 # 最多动画帧数

# 创建图形
fig, ax = plt.subplots(figsize=(7, 7))
ax.set_aspect('equal')
ax.set_xlim(-1.3, 1.3)
ax.set_ylim(-1.3, 1.3)
ax.set_title("割圆法动画演示：多边形逼近圆周率 π", fontsize=14)

# 添加单位圆
circle = plt.Circle((0, 0), radius, fill=False, linestyle='--', color='gray')
ax.add_patch(circle)

# 多边形对象和文本对象
polygon_line, = ax.plot([], [], 'b-', linewidth=2)
info_text = ax.text(-1.25, 1.18, '', fontsize=11, color='darkred', fontfamily='monospace')
formula_text = ax.text(-1.25, -1.2, '', fontsize=10, color='black', fontfamily='monospace')

def generate_polygon(n):
    """生成正n边形的顶点"""
    angles = np.linspace(0, 2 * np.pi, n + 1)
    x = radius * np.cos(angles)
    y = radius * np.sin(angles)
    return x, y

def update(frame):
    n = init_n * (2 ** frame)
    x, y = generate_polygon(n)
    polygon_line.set_data(x, y)

    # π近似计算：π ≈ n × sin(π / n)
    pi_approx = n * np.sin(np.pi / n)

    info_text.set_text(f"边数: {n:5d}     π ≈ {pi_approx:.10f}")

    # 显示公式推导
    formula_text.set_text(
        "π ≈ n × sin(π / n)     (r = 1)\n"
        "推导：L = n × s = 2n × sin(π / n) → π ≈ L / 2\n"
    )

    return polygon_line, info_text, formula_text

# 动画制作
ani = animation.FuncAnimation(fig, update, frames=max_frame, interval=1000, blit=True)
plt.show()