怎样用尺规作图法把一个圆等分成7份

2025-03-16 13:21:29
推荐回答(2个)
回答(1):

这在建筑工程制图里是个很经典的作业
1.以圆心为坐标原点,建立坐标系
2.以Y轴上方与圆的交点为圆心,前一个圆的直径为半径做圆,交X轴与两点A
B
3.把小圆的Y轴直径7等份等份点1
2
3
4
5
6
7
8

4.连接2AB
3AB
4AB
……7AB;
5.把圆上各点连接即得!!
作圆内接任意多边形(以七边形为例)
(1)
将直径AB七等分;
(2)
以B为圆心,BA为半径作圆弧,交水平中心线于M和N两点;
(3)
M和N分别与各奇数点(1,3,5点)连接,连线分别交圆周于Ⅰ,Ⅱ,Ⅲ和Ⅴ,Ⅵ,Ⅶ点.
(注意,作奇数边多边形时连奇数等分点,作偶数多边形时则连偶数等分点);
(4)依次连接Ⅰ,Ⅱ,Ⅲ,B,Ⅴ,Ⅵ,Ⅶ点,即得正七边形。

回答(2):

在与圆o的直径ab垂直的半径oc上,作出oc的中点d,在ob上作一点e,使oe等于半径的1/8;以e为圆心,ed长为半径作弧,与oa、ob分别交于f、g;以f为圆心,fd长为半径作弧,交oa延长线于h,以g为圆心,gd长为半径作弧,交oa于i;作ob中点j,以线段ij为直径作圆,交oc于k;过k作ab的平行线,与以线段oh为直径的圆交于远端l,过l作oc的平行线,与圆o交于m。弧am就是圆o的1/17

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