直角�들의 連結에서 보이고 있는 特殊한 性質에 관하여 = On the Special Properties visible in the Connections of Right Angle-hooks

다국어 초록 (Multilingual Abstract)

G. Howson and B. Wilson, coauthors of the book "School Mathematics in 1990s", stated as follows: "It is not by chance that mathematicians tend to mature and achieve fame earlier than, say, biologists or historians. For a school student can already operate at school in much the same way as a professional mathematician...". They pointed out further, that the way students solve mathematics problems (-where a big part belongs to germetry-) is so to speak a scientific one. But we teach mathematics not only to gifted students, but with good reasons to everybody. Students shall get an exemplary idea of what "scientific work in the abstract" is. And an easy way to this aim is to put their minds to mathematics, and within mathematics, the easiest way of learning principles of scientific work is to tackle geometric problems."
Thus students may learn the principles of a mathematical proof, develop a feeling for how to deduce a fact from evident facts-axioms, and finally they might become aware for hidden assumptions (e.g. the Euclidean structure).
Another, and a quite important facet of geometric problems is that students stimulate "geometric fantasy." If we do in this way, we can then train how to guess and find analogous theorems or generalisations.
In my opion a third component is the aesthetic facet of geometry. The theorems for themselves are marvellous mathematical gems; their proofs-if there are different ways of proving them - have different aesthetic quality which students should become able to realize.
Next let us make mention of my treatise. The most important core of this treatise is following: If two opposite-similar isosceles right angles are linked at one leg's endpoint, then their vertices and the center of the line segment defined by the free leg's endpoint form and isosceles right angle.
This little theorem gives rise to many generalisations and applications, which range from elementary triangle-geometry to conformal kinematics and to practical geometry. This treatise's didactical aim is to practice the mathematical principle of generalisation and to suggest independent research work.

목차 (Table of Contents)

• Ⅰ. 序論
• Ⅱ. 本論
• A. 한 雙의 直角에 관한 중요한 性質들
• B. 正四角形들의 餘雙들
• C. 正四角形들의 프랙탈 樹形과 그 分枝들
• D. 直角�들과 外및 內正四角形들의 閉트리플렛
• Ⅲ. 結論
• 參考文獻
• 英文要約