sairate
7b9ed30185
- 新增 jiyi.py 文件，实现字母翻牌记忆游戏功能 - 添加 youxijiemian.py 文件，创建游戏开始界面 - 使用 turtle 和 tkinter 模块分别实现游戏和界面 - 支持选择不同难度的游戏模式
54 lines
1.5 KiB
Python
54 lines
1.5 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.animation as animation
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# 圆的半径
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radius = 1.0
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init_n = 6
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max_frame = 10 # 最多动画帧数
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# 创建图形
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fig, ax = plt.subplots(figsize=(7, 7))
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ax.set_aspect('equal')
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ax.set_xlim(-1.3, 1.3)
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ax.set_ylim(-1.3, 1.3)
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ax.set_title("割圆法动画演示：多边形逼近圆周率 π", fontsize=14)
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# 添加单位圆
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circle = plt.Circle((0, 0), radius, fill=False, linestyle='--', color='gray')
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ax.add_patch(circle)
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# 多边形对象和文本对象
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polygon_line, = ax.plot([], [], 'b-', linewidth=2)
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info_text = ax.text(-1.25, 1.18, '', fontsize=11, color='darkred', fontfamily='monospace')
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formula_text = ax.text(-1.25, -1.2, '', fontsize=10, color='black', fontfamily='monospace')
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def generate_polygon(n):
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"""生成正n边形的顶点"""
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angles = np.linspace(0, 2 * np.pi, n + 1)
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x = radius * np.cos(angles)
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y = radius * np.sin(angles)
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return x, y
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def update(frame):
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n = init_n * (2 ** frame)
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x, y = generate_polygon(n)
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polygon_line.set_data(x, y)
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# π近似计算：π ≈ n × sin(π / n)
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pi_approx = n * np.sin(np.pi / n)
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info_text.set_text(f"边数: {n:5d} π ≈ {pi_approx:.10f}")
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# 显示公式推导
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formula_text.set_text(
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"π ≈ n × sin(π / n) (r = 1)\n"
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"推导：L = n × s = 2n × sin(π / n) → π ≈ L / 2\n"
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)
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return polygon_line, info_text, formula_text
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# 动画制作
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ani = animation.FuncAnimation(fig, update, frames=max_frame, interval=1000, blit=True)
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plt.show()
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