图解法求实长方法的变换推广及“形”“数”关系分析

Transformation Promotion of Graphical Method for Real Long and Relationship between Shape and Number

图解法求实长的方法有三种,即旋转法、直角三角形法和换面法。三种方法既有联系又有区别,虽然作图形式不同,但三种作图方法的原理一致:都是依据正投影原理及直线的投影特性来求得实长,三种求实长方法的实质相同:直线AB的实长等于其三个几何尺度的平方根,即AB=(△X)2+(△Y)2+(△Z)2姨。三种方法互为变式:直角三角形法是换面法的简化形式,换面法是直角三角形法的一般形式,旋转法则可看成是直角三角形法和换面法的最简形式。三种方法中直角三角形法应用最广。三种方法都可以利用直角三角形的性质及代数计算来加以证明。

There are three graphic methods for real long,rotation method,right triangle method,changing surface method,there are relation and difference among three methods,though different forms of drawing method,principles of them are same,which are according to front-projection and linear projection to get real long. The essences of three methods for real long are same,long of linear AB is equal to the square root of the three geometric dimensions,namely,AB= （△X）2＋（△Y）2＋（△Z）2 . Three methods are variable types each other：a right triangle method is simplified form of changing surface method,a changing surface method is general form of right triangle method,the rotating method is the simplest form of right triangle method and changing surface method. A right triangle method is the most widely used in three kinds of methods. Three methods can be proved using the feature of a right triangle and algebraic computation.