怎么用没有刻度的尺和一把普通圆规画出一个正十七边形?

2024-11-19 08:23:23
推荐回答(3个)
回答1:

步骤一: 

  给一圆O,作两垂直的直径OA、OB, 

  作C点使OC=1/4OB, 

  作D点使∠OCD=1/4∠OCA, 

  作AO延长线上E点使得∠DCE=45度。 

  步骤二: 

  作AE中点M,并以M为圆心作一圆过A点,此圆交OB于F点,

  再以D为圆心,作一圆过F点,此圆交直线OA于G4和G6两点。 

  步骤三: 

  过G4作OA垂直线交圆O于P4, 

  过G6作OA垂直线交圆O于P6, 

  则以圆O为基准圆,A为正十七边形之第一顶点P4为第四顶点,P6为第六顶点。 

  以1/2弧P4P6为半径,即可在此圆上截出正十七边形的所有顶点

回答2:

在梁绍鸿编、赵慈庚校的《初等数学复习及研究》(人民教育出版社1978年7月一版第6次印刷)423—428页载有详细的推证和作法。单说作法仅占两页篇幅.因要画图,符号也颇复杂,我不可能在这里给你做了,你可看看这本书。如果你感兴趣而又找不到此书,请提供准确通讯地址我给你复印后寄奉。
正17边形的作图方法是德国数学家高斯(1777--1855)于1796年首先发现的.到目前为止有多种方法.上面所引这本书中采用的方法是出自<数学通讯>1954年5月号上所载欧阳琦的一篇文章<正十七边形作图法>,你如有兴趣可到图书馆查阅这篇资料.

回答3:

王军团大哥我膜拜你,顶礼膜拜……

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