幾何教材の背景としての線形理論 : 相似と相似変換

Linear Theory as a Background of Geometric Teaching Materials : Similarity and Similar Transformations

今岡 光範

広島大学教育学部紀要. 第二部

Bulletin of the Faculty of Education, Hiroshima University. Part 2

In this paper, we show a process of similarity in the framework of linear theory. Similarity of figures is one of the fundamental concepts in Euclidean geometry, and an elementary definition of it uses the notion of a site or a center of similarity. Another definition of similarity is given using a similar transformation, which enables us to consult methods developed in linear algebra. We investigate a relation between such definitions, and the effect of the comparison. Main subjects include the following:

How to find a cite and a center of similarity for given similar figures;

how to apply properties of the orthogonal transformation to the study of similarity.

Linear algebra is a well investigated subject in mathematics, which has given us an abundant idea for linear theory. The purpose of our study is to describe functions of linear algebra as a background of fundamental properties of figures.

教育 [ 370 ]

日本語

広島大学教育学部

[ISSN] 0440-8713

[NCID] AN0021336X