美国百年几何教科书中的棱柱定义  

Definitions of the Prism in Geometry Textbooks from 1829 to 1929

作　　者：洪燕君[1,2] 汪晓勤[1] 

机构地区：[1]华东师范大学数学系,上海200241 [2]石河子大学师范学院,新疆石河子832000

出　　处：《数学教育学报》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)

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.

关 键 词：几何教科书 棱柱 欧几里得定义 棱柱面定义 

分 类 号：G40-059.3[文化科学—教育学原理]