绝对度量:非欧几何的开端  

Absolute Measure: the Beginning of non-Euclidean Geometry

作　　者：郭婵婵 GUO Chan-chan(Institute for Advanced Study of the History of Science,Northwest University,Xi'an 710127;School of Mathematics and Computer Science,Yan’an University,Yan'an 716000,China)

机构地区：[1]西北大学科学史高等研究院,西安710127 [2]延安大学数学与计算机科学学院,延安716000

出　　处：《自然辩证法研究》2020年第3期91-96,共6页Studies in Dialectics of Nature

基　　金：陕西省教育厅专项科学研究计划“罗巴切夫斯基非欧几何中的度量问题研究”(19JK0973);国家自然科学基金资助项目“代数方程之Galois理论的若干历史问题研究”(11571276),“非欧几何学早期历史的研究与普及”(11926501)。

摘　　要：非欧几何的建立源于平行公设证明问题的解决过程,是数学家描述物理空间相对应几何的结果。从度量的角度审视非欧几何的创立过程,分析先驱者和创立者的具体工作。19世纪前数学家已意识到,承认存在长度绝对度量与否,是区分非欧几何与欧氏几何的关键。罗巴切夫斯基和波约考虑到不同尺度的空间具有不同的几何,在允许长度绝对度量的基础上建立了非欧几何。The establishment of non-Euclidean geometry stems from the process of solving the problem of proving Parallel Postulate as a theorem,and it is also the result of mathematicians finding the geometry which can describe the physical world.The birth of non-Euclidean geometry was elaborated from the perspective of measurement,and work of the forerunners and founders of non-Euclidean geometry were analyzed in this paper.Mathematicians before 19 th century had recognized the key difference between non-Euclidean and Euclidean geometry is whether to admit the existence of absolute measure of length or not.Lobachevsky and J.Bolyai considered that different scale of space has different geometry and established non-Euclidean geometry on the assumptions of the existence of absolute measure of length simultaneously.

关 键 词：绝对度量 平行公设 罗巴切夫斯基 波约 非欧几何 

分 类 号：N09[自然科学总论—科学技术哲学]