点到平面距离公式的七种推导方法探讨

摘要

研究“点到平面的距离公式’’的推导方法，得出7种可行的证法，不同的证法证明过程复杂程度不一样，简单的证明方法可绕过“法式方程”、“离差”，“向量运算”，仅用“直线的参数方程”和一些旧识就可证明。这些证法可作为教材编写或教师教学时参考，也可作为培养学生发散思维之用。%This thesis studies derivation methods of ＂from point to plane＂ and seeks to get the result of seven practicable proofs of it. Even though the ＂French-style equation＂ and ＂the deviation＂ can＇t be applied, the seven derivation methods above can demonstrate the corresponding knowledge just by means of ＂vector and its projection＂ and some used knowledge. These proof methods can be used as textbooks or teaching for reference, at the same time, they can be used to train the thinking flexibility of students.