対角線から見た四角形

• 垣水 修

  新潟大学教育学部

書誌事項

タイトル別名

• Quadrilaterals Seen from Their Diagonals

抄録

In this paper we study quadrilaterals via the study of the diagonals. We think that the study which observes diagonals is important for the study of figures. The unification view will be brought to the curriculum by it. Furthermore, we discuss lessons "which acts to the heart and soul so that soap may act on clothes exactly". <br>　　A quadrilateral has two diagonals. The character of the quadrilateral is closely reflected in the relation of these two diagonals. It is important to constitute the curriculum from this viewpoint. The fundamental relations about the diagonals of a quadrilateral are the following: <br>　　(a) The length of two diagonals is equal. <br>　　(b) Two diagonals cross perpendicularly. <br>　　(c) Two diagonals bisect others mutually. <br>Table A summarizes character of diagonals of four typical classes of quadrilaterals. <br><br>Table A<br><br>　　We think that the viewpoint as which we regard a curriculum and lessons as follows. quadrilateral from its diagonals can be harnessed in the <br>(1) In elementary school mathematics, it is important to understand Table A by operational activities. Furthermore, it is possible to combine the viewpoint of tiling by a quadrilateral and comparison of area. We give and examine such an example. <br>(2) In junior high school mathematics, it is important to understand the proof of Table A. Moreover, it is important to utilize it. We give the examples of quadrilaterals which satisfy the properties (a) and (b), but not (c), and then examine several properties of them by using Table A. <br>(3) In high school mathematics, it is important to regard the diagonals as vectors. Moreover, by using the inner product of vectors and trigonometry, we can study general quadrilaterals. Ptolemy' s theorem is taken up from this viewpoint.

収録刊行物

• 数学教育学研究 : 全国数学教育学会誌

  数学教育学研究 : 全国数学教育学会誌 14 (0), 1-8, 2008

  全国数学教育学会

キーワード

• 対角線
• 四角形
• 幾何学

詳細情報

• CRID: 1390845713042971776
• NII論文ID: 110009498607
• DOI: 10.24529/jasme.14.0_1
• ISSN: 24333034
• ISSN: 13412620
• 本文言語コード: ja
• データソース種別:
  • JaLC
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可