用python求解数学题

 

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

def generate_circle_points(center_x, center_y, radius, num_points=100):
    points = []
    for i in range(num_points):
        #把圆360°拆分成num_points个角度
        angle = 360 * i / num_points
        #循环迭代每个角度得到圆边上的所有坐标点D
        x = center_x + radius * math.cos(angle)
        y = center_y + radius * math.sin(angle)
        points.append((x, y))
    return points

#找到BD的所有中心点坐标
def find_midpoint(point1, point2):
    return ((point1[0] + point2[0]) / 2, (point1[1] + point2[1]) / 2)

#方法一，使用math库的sqrt函数：计算所有BD线上的中心点到原点(0,0)的距离
# def calculate_distance(point1, point2):
#     return math.sqrt((point1[0] - point2[0]) ** 2 + (point1[1] - point2[1]) ** 2)

#方法二，使用numpy库的norm函数计算向量的长度：计算所有BD线上的中心点到原点(0,0)的距离
def calculate_distance(point1, point2):
    vector = np.array([point1, point2])
    return np.linalg.norm(vector)

if __name__ == "__main__":
    # A点的坐标
    A_x, A_y = 0, 6

    # B点的坐标
    B_x, B_y = 2 * math.sqrt(7), 0

    # C点的坐标
    C_x, C_y = 0, 0

    # 以A为圆心的圆的半径
    radius = 2

    # 找出以A为圆心的圆边上的所有点D
    D_points = generate_circle_points(A_x, A_y, radius)

    # 找到B点和每个点D之间的线的中心点F
    F_points = [find_midpoint((B_x, B_y), D) for D in D_points]

    # 计算所有F点和C点之间的距离，并找到最长和最短距离
    min_distance = float('inf')
    max_distance = 0.0
    #循环迭代所有F点到C点的距离，找到最短、最长的距离。
    for F in F_points:
        distance = calculate_distance(F, (C_x, C_y))
        min_distance = min(min_distance, distance)
        max_distance = max(max_distance, distance)

    # 输出结果
    print("F点和C点的最短距离是: {:.0f}".format(min_distance))
    print("F点和C点的最长距离是: {:.0f}".format(max_distance))

    # 绘制图形
    plt.figure(figsize=(8, 8))

    # 画圆
    circle = plt.Circle((A_x, A_y), radius, color='b', fill=False)
    plt.gca().add_patch(circle)

    # 画点A、B、C
    plt.scatter([A_x, B_x, C_x], [A_y, B_y, C_y], c='red', label='A, B, C')

    # 画线
    plt.plot([A_x, B_x],[A_y, B_y])
    plt.plot([A_x, C_x],[A_y, C_y])
    plt.plot([B_x, C_x],[B_y, C_y])
    
    # 画点D和F
    D_x, D_y = zip(*D_points)
    F_x, F_y = zip(*F_points)
    plt.scatter(D_x, D_y, c='green', label='D')
    plt.scatter(F_x, F_y, c='orange', label='F')

    # 添加标签
    plt.text(A_x, A_y, 'A', ha='right', va='bottom')
    plt.text(B_x, B_y, 'B', ha='right', va='bottom')
    plt.text(C_x, C_y, 'C', ha='right', va='bottom')
    plt.text(D_x[0], D_y[0], 'D', ha='right', va='bottom')
    plt.text(F_x[0], F_y[0], 'F', ha='right', va='bottom')

    plt.xlabel('X')
    plt.ylabel('Y')
    plt.title('Circle with points A, B, C, D, F')
    plt.legend()

    # 设置坐标轴范围
    plt.xlim(-5, 10)
    plt.ylim(-5, 10)

    # 显示图形
    plt.grid()
    plt.axhline(y=0, color='k', linewidth=0.5)
    plt.axvline(x=0, color='k', linewidth=0.5)
    plt.gca().set_aspect('equal', adjustable='box')
    plt.show()

 

得出结果：