在欧几里得(Euclid)平面上建立对偶原则的一种方法

本文主要就欧氏平面的特征,介绍一种在欧氏平面上建立对偶原则的方法。首先,在欧氏平面上,建立不过原点的直线M;x_0x+y_0y—1=0与点M(x_0,y_0)(?)(0,0)之间的对偶对应。然后根据这种对应阐明初等几何中仅与度量性质有关而本身并无联系的两个命题能够对偶地联系起来。

A Method of Establishing Duality Principle for Euclidean Plane

It is well known that the duality principle on projective Geometry does not hold in Euclidean Geometry. In this paper, firstly, we will Establish the dual Correspondence between the point which is not origin and the line which do not pass through origin by: X_0X+y_0y-1=0(?)(x_0,y_0). Secondly, we give duality principle on Euclidean plan: A metrical theorem remains valid if we interchange the Concepts of point and line which are dual mutually. Finally, we give several interest examples.