解题方法
1 . 三国时代吴国数学家赵爽所注《周髀算经》中给出了勾股定理的绝妙证明.下面是赵爽的弦图及注文,弦图是一个以勾股形之弦为边的正方形,其面积称为弦实.图中包含四个全等的勾股形及一个小正方形,分别涂成红(朱)色及黄色,其面积称为朱实、黄实,利用
勾×股+(股-勾)
朱实+黄实=弦实,化简得勾
股
=弦
.设勾股形中勾股比为
,若向弦图内随机抛掷1000颗图钉(大小忽略不计),则落在黄色图形内的图钉数大约为( )
![](https://img.xkw.com/dksih/QBM/2020/12/9/2610363660984320/2613128745107456/STEM/dc546d92-8d11-4c19-aaed-7f7e8de95385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e461727449e22cdf9d0ba260952e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e709298207cf8c851dfb947b4d9287a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564b8d5e56d663f0703474b95a409b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921ef5abce73648e3834140df9a72aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921ef5abce73648e3834140df9a72aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d65e051e943ab28fa57aee2fb57994.png)
![](https://img.xkw.com/dksih/QBM/2020/12/9/2610363660984320/2613128745107456/STEM/dc546d92-8d11-4c19-aaed-7f7e8de95385.png)
A.800 | B.866 | C.134 | D.200 |
您最近一年使用:0次
2 . 如图所示的是希腊著名数学家欧几里德在证明勾股定理时所绘制的一个图形,该图形由三个边长分别为
,
,
的正方形和一个直角三角形围成,现已知
,
,若从该图形中随机取一点,则该点取自其中的阴影部分的概率为
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/9b352b2e-9374-4417-9ba9-727900afd56f.png?resizew=155)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/9b352b2e-9374-4417-9ba9-727900afd56f.png?resizew=155)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次