摘要
1829—1929年出版的70种美国中学几何教科书中先后给出了棱柱的6种定义,即欧几里得的定义、改进的欧氏定义、基于棱锥的定义、基于棱的定义、基于棱柱面的定义和基于棱柱空间的定义.尽管欧几里得的定义存在缺陷,但由于《几何原本》的深刻影响,该定义在很长时间里一直为教科书所广泛采用;直到19世纪末,才出现多种定义并存的现象,最终,棱柱面定义和改进的欧氏定义逐渐取代了旧定义.棱柱定义的百年演变反映了人们对棱柱概念由直观到严谨的认识过程,为今日教科书编写和课堂教学提供了一面镜子.
This paper analyzes the prism definitions in 70 US geometry textbooks from 1829 to 1929, namely, Euclid＇s definition, improved Euclidean definition, definitions based on the pyramid, the edge, the prismatic surface and the prismatic space. Due to the far-reaching impact of The Elements, the Euclid＇s definition, though not perfect, had remained in textbooks for a long time. Not until the end of 19 century, did a variety of definitions coexist. In the end, the improved Euclidean definition and the definition based on the prismatic surface took the place of the old ones. The history of prism definition reveals that our understanding on prism has experienced a gradual process, from intuitive to rigorous, which might provide some inspiration for today＇s prism teaching.
出处
《数学教育学报》
CSSCI
北大核心
2016年第5期67-72,共6页
Journal of Mathematics Education
基金
人教社课程与教材研究所“十二五”规划课题——数学史融入数学教材研究(KC2014—010)
关键词
几何教科书
棱柱
欧几里得定义
棱柱面定义
geometry textbook
prism
Euclidean definition
the definition based on the prismatic surface
