1 . 斐波那契螺线又叫黄金螺线,广泛应用于绘画、建筑等,这种螺线可以按下列方法画出:如图,在黄金矩形
(其中
)中作正方形
,以F为圆心,AB长为半径作圆弧
;然后在矩形CDEF中作正方形DEHG,以H为圆心,DE长为半径作圆弧
;……;如此继续下去,这些圆弧就连成了斐波那契螺线.记圆弧
,
,
的长度分别为
,
,
,给出以下两个命题:
,
.则下列选项为真命题的是( )
![](https://img.xkw.com/dksih/QBM/2022/3/19/2939720919900160/2940246458572800/STEM/450a9818442246d3a368fd74b431aeba.png?resizew=218)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924dce7607481d800ab87ad445589af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be3f37b98f1c27fa1304ec7e463df90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fa3297d4d7737883739bb97110ecdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be3f37b98f1c27fa1304ec7e463df90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fa3297d4d7737883739bb97110ecdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569f63c517a8a7dbf5cf85d849e87d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a405282cf48dcf631fa5d550928f6504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66ec0f128897452756472714e997259.png)
![](https://img.xkw.com/dksih/QBM/2022/3/19/2939720919900160/2940246458572800/STEM/450a9818442246d3a368fd74b431aeba.png?resizew=218)
A.![]() | B.![]() |
C.![]() | D.![]() |
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