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在中学数学敎学法(伯拉基斯著吳品三譯)第四册几何敎学法46頁的第二行提到“兩个角也可以是不可通約的,例如,在埃及三角形中的角(所謂埃及三角形,即以3,4,5为边的三角形)。”关于这一結論的証明原書只指出了参考文件,但一般也不易查到。本文目的是要說在什么情况下的直角三角形三內角之間可通約,在什么情况下的直角三角形三內角之間不可通約,而埃及三角形內角之間不可通約便当作本文的特例而解决了。为此目的,我們先作如下的一般討論。
In the second line of the 46th page of the geometrical dropout method in the fourth volume of the mathematics dropout method for middle school mathematics (Translation by Barakis), “The two corners can also be incommensurable, for example, in the corner of an Egyptian triangle. (The so-called Egyptian triangle, which is a triangle with 3, 4, and 5 sides.) ”The proof of this conclusion, the original book only pointed out the reference documents, but it is generally not easy to find. The purpose of this paper is to say under what circumstances the three internal angles of right triangles can be approximated, and under what circumstances the three internal angles of right triangles cannot be approximated, and the incommensurability between the internal angles of the triangular triangles is considered as The special case was solved. For this purpose, we first make the following general discussion.