Question

正九边形尺规做图

Answer 1

更新1:

根据高x的理论 质数边形尺规做图要是2^2t+1 >100只有3、5、17 冇9

更新2:

高斯

更新3:

izayoi_ami 唔知就唔好嘈la 我画个，纯用圆规加直线(唔系尺)就得 如果要用有刻度的工具就唔会问la

更新4:

ckcwow 我有《典雅的几何》手

更新5:

画一个六角星用点1
2
3做圆心穿过六角星中六角形的两点，

尺规作图 的用的 尺和规 也是 没有刻度 所谓"做不出来" 是指 利用 没有刻度 的 工具去作图... (数学用语是 不可构造) 使用有刻度的工具 把任意的角分三等份 是极其简单的 然而若要使用 没刻度的工具
那麽连简单的 60度也不能将之三等份 (即是说 20度角是不可构造) 正九边形的作图法 牵涉 把已知角 分三等份 (正九边形 内角为 140) 如有方法 可以不使用 没有刻度的工具构造出 正九边形 即是说 140度 的角是 可构造的 那麽与其 互补的 40度的角也是可构造 另一方面
任意角可使用没刻度的工具二等分 亦即是说 20度 是可构造 有矛盾 2009-04-28 23:20:06 补充： 问人野请你礼貎d 好wor... b
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 补充： If you really want to know
please list out the detail of your construction rather than just giving a plete diagram 2009-04-29 00:37:30 补充： 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 补充： 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 补充： 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 补充： 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 补充： 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 i436.photobucket/albums/qq89/iveshoot/9-gon 2009-04-29 15:26:39 补充： 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) i436.photobucket/albums/qq89/iveshoot/9-gon2 However
you can see that the length of o sides are not equal
或许你直接参阅《典雅的几何》，便不会有此问题。 相信书中提出的只是一种近似的作图法，可参考： johnmay.wordpress/2008/07/31/construction-of-regular-polygons/
「p.1的正九边形尺规做图有什么问题?」是甚么意思？ 是你尝试绘制正九边形出现了一些小问题，导致你不成功？ 还是其他？