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单词 Geometric Construction
释义

Geometric Construction

中文百科

尺规作图 Compass-and-straightedge construction

(重定向自Geometric Construction)
正五边形的作图
作图公法

尺规作图(英语:Compass-and-straightedge 或 ruler-and-compass construction)是起源于古希腊的数学课题。只使用圆规和直尺,并且只准许使用有限次,来解决不同的平面几何作图题。

值得注意的是,以上的“直尺”和“圆规”是抽象意义的,跟现实中的并非完全相同,具体而言,有以下的限制:

尺规作图的研究,促成数学上多个领域的发展。好些数学结果就是为解决古希腊三大名题而得出的副产品,对尺规作图的探索推动了对圆锥曲线的研究,并发现了一批著名的曲线。

若干著名的尺规作图已知是不可能的,而当中很多不可能的例子是利用了19世纪出现的伽罗瓦理论以证明。尽管如此,仍有很多业余爱好者尝试这些不可能的题目,当中以化圆为方及三等分任意角(Angle trisection)最受注意。

英语百科

Compass-and-straightedge construction 尺规作图

(重定向自Geometric Construction)
Creating a regular hexagon with a straightedge and compass
Construction of a regular pentagon
A compass

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with collapsing compass; see compass equivalence theorem.) More formally, the only permissible constructions are those granted by Euclid's first three postulates. Every point constructible using straightedge and compass may be constructed using compass alone.

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更新时间:2025/6/18 18:42:40