拉格朗日乘数法在几何中的几点应用

Applications of Lagrange Multiplier Method in Space Analytic Geometry

利用求多元函数极值的拉格朗日乘数法,推导了点到直线、点到平面及两异面直线间的距离公式,并推导了椭球面上平面截线的面积公式。

By using the Lagrange multiplier method to find the extreme values of multivariate function, the distance formulas from a point to a straight line, a point to a plan and between two nocoplanar straight lines were established. The area formulas Of the plan sections on an ellipsoidal surface were deduced.