【摘要】 我们指出一类中学平面几何问题与大学静电学的镜像法存在相通的数学本质:由于球对称性以及相似三角形的性质,除球心之外的球内任一点在球外都存在对偶点,这两点到球面上任意点的距离之比都不变。这个范例对中学数理化与大学物理之间衔接的教学实践具有一定的启发意义。更多还原

【Abstract】 We point out that a class of high-school plane-geometry problems share the same mathematical nature with the method of image charges in college electromagnetic courses: For any point(except for the center) inside a sphere there exists a geometric-dual point outside the sphere; the ratio of the distances from these two points to any point on the sphere is a constant. This property is due to the spherical symmetry and the property of similar triangles. This heuristic example can be used to link the high school and college physics educations.更多还原