✔ 最佳答案
尺規作圖 的用的 尺和規 也是 沒有刻度
所謂"做不出來" 是指 利用 沒有刻度 的 工具去作圖...
(數學用語是 不可構造)
使用有刻度的工具 把任意的角分三等份 是極其簡單的
然而若要使用 沒刻度的工具 , 那麽連簡單的 60度也不能將之三等份
(即是說 20度角是不可構造)
正九邊形的作圖法 牽涉 把已知角 分三等份
(正九邊形 內角為 140)
如有方法 可以不使用 沒有刻度的工具構造出 正九邊形
即是說 140度 的角是 可構造的 那麽與其 互補的 40度的角也是可構造
另一方面 , 任意角可使用沒刻度的工具二等分
亦即是說 20度 是可構造
有矛盾
2009-04-28 23:20:06 補充：
問人野請你禮貎d 好wor...
btw, logically, your construction is impossible , (please find a book to read about the angle of 20 degree is not constructible)
I believe your construction use approximation rather than exact.
2009-04-28 23:20:10 補充：
If you really want to know, please list out the detail of your construction rather than just giving a complete diagram
2009-04-29 00:37:30 補充：
The next step is then, how can you draw the hexagram without measurement?
{Note: If you can do so, you can then trisect a given segment namely the side of the equilateral triangle}
2009-04-29 00:55:53 補充：
p.s.
you can construct it from a hexagon and draw equilateral triangle on each part
{those steps should be ok}
now the remaining is to verify whether you can draw,
I will give you the detail tomorrow
2009-04-29 14:31:17 補充：
In terms of construction, 3 points forms a circle, so those circles are constructible.
Finally, why do you believe the 9-gon is regular? If so, prove it.
2009-04-29 14:53:11 補充：
Indeed, none of the interior angle is 140 degree.
{This is argued as above, the impossibility of 20 degree is a result from algebra}
However, if you don't like a proof from algebra, just use simple co-geom to solve the angle or do an accurate drawing.
2009-04-29 15:11:47 補充：
If you still don't figure out what the problem is,
look at the below image file
This is an exact figure of what you said with AB=1 unit
http://i436.photobucket.com/albums/qq89/iveshoot/9-gon.jpg
2009-04-29 15:26:39 補充：
Yhe construction you mentioned is simply wrong
However, if we draw the 6 circles and choose one point from produced
a more accurate 9-gon can be constructed (the blue one)
http://i436.photobucket.com/albums/qq89/iveshoot/9-gon2.jpg
However, you can see that the length of two sides are not equal
