题目如图1,P是等边三角形ABC内一点,且PA=n,PB=m,PC=t,求△ABC的面积S_(△ABC)。1975年,美国的一本数学刊物上刊登了这个问题,由于题目非常简洁,通俗易懂,问题一提出就激起了广大数学爱好者的强烈兴趣,不久就有人提出了一个解法,但思路之奇特,方法之怪异,足以让人望而却步。近年来,国内的一些杂志上也出现过类似的问题。初看这道题目,似乎平平淡淡,并无特别之处,但一尝试,发现 The problem is shown in Fig. 1. P is a point in the equilateral triangle ABC, and PA = n, PB = m, PC = t. Find the area S_(△ABC) of △ABC. In 1975, this issue was published in a mathematics publication in the United States. Because the topic was very concise and easy to understand, the question raised aroused strong interest among math enthusiasts. Someone soon proposed a solution, but the train of thought Odd, strange methods, enough to make people prohibitive. In recent years, similar problems have appeared in some domestic magazines. At first glance, this topic seems to be unimpressive. There is nothing special about it.