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课件实例|2.10化圆为方

  • 2026-04-17 02:45:35
课件实例|2.10化圆为方

把圆等分后转化为长方形,直观演示化圆为方的过程。

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通过点的旋转构造扇形,利用深度迭代绘制圆,借助拉杆显示化圆为方的动态过程。

1.制作等分拉杆及度量点值

构造线段AB,构造线段AB的中点C,构造线段AB上的动点D,颜色改为绿色。隐藏线段AB,构造线段AC和线段CB。

选择点D和线段AC,按“shift”键,点击【度量】→【点的值】,得到“D在AC上”。同上步骤度量点D在线段CB上的点值。如图2-10-1。

图2-10-1

2.建立参数及公式

新建参数“t1=4”,编辑得到如下公式:  

3.构造扇形模型

(1)构造圆

构造线段EF,构造任意点G,点G垂直向上平移1cm,得到点G',构造射线GG'。选中点G和线段EF,点击【构造】→【以圆心和半径绘圆】。如图2-10-2。

图2-10-2

(2)构造上半模型

构造圆和射线的交点H,隐藏圆、射线及点G'。双击点G为旋转中心,将点H分别旋转“360°/(t1*4)*0.5”和“-360°/(t1*4)*0.5”角度,得到点H'和点H''。如图2-10-3。

图2-10-3

(3)构造下半模型

双击点G为旋转中心,将点H'、H、H''旋转180°,得到点X、Y、Z。

构造点I,依次选中点G和点I,点击【变换】→【标记向量】,选中点X、Y、Z,按标记向量进行平移。如图2-10-4。隐藏点X、Y、Z。

图2-10-4

4.构造扇形及迭代(左上部分)

(1)构造扇形

构造点J、点K,以点J为旋转中心,将点K旋转“360°/(t1*4)”角度,得到点K'。以点K'为旋转中心,将点J旋转“-D在 AC上*(360°/(t1*4))”角度,得到点J'。  

依次选中点J、点K、点K',点击【构造】→【圆上的弧】,选中弧线KK',点击【构造】→【弧内部】→【扇形内部】。

(2)迭代扇形

选中点J,点K,参数t1=4,按住“shift”键,点击【变换】→【深度迭代】,选择点J'和点K'为初象,进行迭代。如图2-10-5。

图2-10-5

5.构造扇形及迭代(右上部分)

(1)构造扇形

构造点L、点M,以点L为旋转中心,将点M旋转“-360°/(t1*4)”角度,得到点M'。以点M'为旋转中心,将点L旋转“D在 AC上*360°/(t1*4)”角度,得到点L'。

依次选中点L、点M'、点M,构造弧MM',构造扇形LMM'内部。

(2)迭代扇形

选中点L、点M,参数“t1-1=3”,按“Shift”键,点击【变换】→【深度迭代】,选择点L'和点M'为初象,进行迭代。如图2-10-6。

图2-10-6

6.构造扇形及迭代(左下部分)

(1)构造扇形

构造点N、点O。以点N为旋转中心,将点O旋转“-360°/(t1*4)”角度,得到点O'。以点O'为旋转中心,将点N旋转“D在 AC上*360°/(t1*4)”角度,得到点N'。

依次选中点N、点O'、点O,构造弧OO',构造扇形NOO'内部。

(2)迭代扇形

选中点O,点N,参数t1-1=3,按“shift”键,点击【变换】→【深度迭代】,选择点O'和点N'为初象,在结构中选择“仅保留非点类对象”。如图2-10-7。

图2-10-7

7.构造扇形及迭代(右下部分)

(1)构造扇形

构造点P、点Q,以点P为旋转中心,将点Q旋转“360°/(t1*4)”角度,得到点Q'。以点Q'为旋转中心,将点P旋转“-D在 AC上*(360°/(t1*4))”角度,得到点P'。

构造弧QQ',构造扇形PQQ'内部。

(2)迭代扇形

选中点P,点Q,参数t1=4,按“shift”键,点击【变换】→【深度迭代】,选择点P'和点Q'为初象,进行迭代。如图2-10-8。

图2-10-8

8.图形的整合

(1)合并到模型

选中点K、点H",点击【编辑】→【合并点】。同上步骤合并点J和点G、点M和点H'、点L和点G、点O和点Z'、点N和点I、点P和点I、点Q和点X'。如图2-10-9。

图2-10-9

(2)关联拉杆

依序选中点G和点H',构造线段GH',右击线段GH',选择“在线段上绘制点”,选中点值“D在CB上”,得到点R。合并点R和点I。如图2-10-10。

图2-10-10

9.调整美观

统一颜色,隐藏不必要的对象。

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  1. CONNECT:[ UseTime:0.000591s ] mysql:host=127.0.0.1;port=3306;dbname=a_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000742s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000329s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000258s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000480s ]
  6. SELECT * FROM `set` [ RunTime:0.000199s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000498s ]
  8. SELECT * FROM `article` WHERE `id` = 460731 LIMIT 1 [ RunTime:0.000410s ]
  9. UPDATE `article` SET `lasttime` = 1777120031 WHERE `id` = 460731 [ RunTime:0.000736s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 66 LIMIT 1 [ RunTime:0.000236s ]
  11. SELECT * FROM `article` WHERE `id` < 460731 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000487s ]
  12. SELECT * FROM `article` WHERE `id` > 460731 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000395s ]
  13. SELECT * FROM `article` WHERE `id` < 460731 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000724s ]
  14. SELECT * FROM `article` WHERE `id` < 460731 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.004553s ]
  15. SELECT * FROM `article` WHERE `id` < 460731 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.002927s ]
0.082121s