提到三边长都是整数的直角三角形,我们往往首先想到的就是边长为“3,4,5”的直角三角形.早在西汉时期,算书《周髀算经》中就有“勾三股四弦五”的记载.其实,我们对“3,4,5”直角三角形进一步探究,还能发现一些有趣且有用的结论.一、基础准备如图1,RtΔABC中,∠C=90°,BC=3,AC=4,AB=5,∠CAB=α,∠CBA=β,显然 Mentioning right-angled triangles whose three sides are all integers, we often think of the right-angled triangles with a side length of 3, 4, 5, etc. As early as in the Western Han Dynasty, the calculations in the calculations of the Zhouyin Sutra had “Hook three shares of four-string five” records. In fact, we further explore the “3,4,5” right-angle triangle, but also found some interesting and useful conclusions. First, the basic preparation shown in Figure 1, RtΔABC , C=90°, BC=3, AC=4, AB=5, ∠CAB=α, ∠CBA=β, obviously