用解析法求解“Philo’s Line”

FIND OUT THE PHILO'S LINE BY ANALYTIC METHOD

从数学分析入手,运用极值原理,找到了“Philo’s Line”在给定条件下的解析表达式,由此解析表达式作出“Philo’s Line”图形.为在铁路、公路、桥梁等工程设计中,确定过定角内一定点并与角的两边相交,且夹在交点间的线段最短的直线,提供了切实可行的方法.

In this paper, the problem of finding the Philo's line is solved by the extreme value principle of mathematical analysis. The analytic expression of the Philo's line in a specific condition is presented. So 'Philo's line' is drawn according to the expression. It gives a method to determine the straight line passing through the stationary point in a given angle, this line overlaps both sides of the angle, and the distance bewteen the points of intersection is the shortest. The method can be used in the design of railway, roads bridges and so on. The an actual example is given.