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圆内接四边形两双对边乘积的和等于其对角线的乘积。这是公元二世纪希腊数学家兼星学家托勒密(Ptolemy)发现的一条美妙的定理,即托勒密定理(以下简称托氏定理)。一千多年来,经过数学工作者们的不断攻究、实践、探索,使得定理的应用遍及中学数学的各个领域,那么托氏定理在解题中为什么能产生如此之功力,发挥如此之效能呢?这里仅就其功能的几个方面作一粗浅的探索,不妥之处,恭请同仁指正。
The sum of the products of the circle inscribed quadrilateral pair is equal to the product of its diagonal. This is a wonderful theorem discovered by Ptolemy, a Greek mathematician and astrologer, in the second century AD, the Ptolemy theorem (hereinafter referred to as the Torquay theorem). For more than a thousand years, through the constant attack, practice, and exploration of mathematicians, the application of the theorem has been applied to all fields of middle school mathematics. So why can Tortrum’s theorem produce such a skill in problem solving? What is wrong with this? Here, we only make a cursory exploration of several aspects of its functions.