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.![]() |
您最近一年使用:0次
2 . 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
中作正方形
,以
为圆心,
长为半径作弧
;然后在黄金矩形
中作正方形
,以
为圆心,
长为半径作弧
;……;如此继续下去,这些弧就连接成了斐波那契螺线.记弧
,
,
的长度分别为
,
,
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2020/11/27/2602061416235008/2605590251945984/STEM/ffd031bb21e34f24a7912d7d85682ab8.png?resizew=146)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f321e2c6fb451dc34196cee9a614a3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b19c646bcb6160197fdf12a9cb31a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36841b80ef629b28b9aa140dfdbde770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770dd9980af04867252bd56ceec3eddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b19c646bcb6160197fdf12a9cb31a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770dd9980af04867252bd56ceec3eddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072f5b724d1ec511d64bc966fa136ad4.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://img.xkw.com/dksih/QBM/2020/11/27/2602061416235008/2605590251945984/STEM/ffd031bb21e34f24a7912d7d85682ab8.png?resizew=146)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
3 . 古代中国的太极八卦图是以圆内的圆心为界,画出相同的两个阴阳鱼,阳鱼的头部有阴眼,阴鱼的头部有阳眼,表示万物都在相互转化,互相渗透,阴中有阳,阳中有阴,阴阳相合,相生相克,蕴含现代哲学中的矛盾对立统一规律.图2(正八边形
)是由图1(八卦模型图)抽象而得到,并建立如图2的平面直角坐标系,设
.则下列错误的结论是( )
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720310018605056/2720901184684032/STEM/172a4529-4b1e-4072-a6f8-dc48164edd5b.png?resizew=439)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720310018605056/2720901184684032/STEM/172a4529-4b1e-4072-a6f8-dc48164edd5b.png?resizew=439)
A.![]() |
B.以射线![]() ![]() |
C.在以点![]() ![]() ![]() ![]() |
D.正八边形![]() ![]() |
您最近一年使用:0次
2021-05-14更新
|
628次组卷
|
4卷引用:山西省太原市2021届高三三模数学(文)试题
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