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初等几何里的作图,允许用的工具是能自由开闭的圆规和无刻度的直尺,若把工具加以限制,如只许用自由开闭的圆规,不许用直尺,便称为圆规作图。本刊1956年第4期孙泽瀛先生已有文章作了详细的研究,本文来研究另一种工具的限制,即只有一个开张成一定角的圆规(不能自由开闭,即半径固定的圆规)和一枝无刻度的直尺,足否也能进行初等几何学里研究的一切作图问题呢? 仔细研究初等几何学之作图,能自由开闭之圆规之功用,不外乎以下四项:
In the drawing of elementary geometry, the tools that are permitted are the compasses that can be freely opened and closed and the rulers without scales. If the tools are limited, for example, only the compasses that can be freely opened and closed, and the rulers are not allowed, they are called compasses. Drawing. In the 4th issue of the 4th issue of this volume, Mr. Sun Zezhao has made detailed studies on this article. This article examines the limitations of another tool, namely that there is only one compass that is opened to a certain angle (cannot be freely opened and closed, ie a compass with a fixed radius) and A ruler without a scale, whether it can also carry out all of the mapping problems studied in elementary geometry? Careful study of the drawing of elementary geometry, the function of the compass can freely open and close, nothing more than the following four: