| 兰伯特的几何学思想探析 |
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| 引用本文： | 郭婵婵.兰伯特的几何学思想探析[J].自然辩证法研究,2022(1):83-89. |
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| 作者姓名： | 郭婵婵 |
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| 作者单位： | 1.延安大学数学与计算机科学学院 |
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| 基金项目： | 延安大学博士科研启动项目(YDBK2020-27);国家自然科学基金资助项目“非欧几何学的若干历史问题研究”(12161086);国家自然科学基金青年科学基金项目“剑桥数学物理学派在流体动力学中的数学物理工作研究”(12101493)。 |
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| 摘 要： | 德国数学家兰伯特在《平行线理论》中通过类比球面提出锐角假设在虚半径球面上成立,这一思想成为后来数学家建立和发展非欧几何的关键.兰伯特在对公理和定义的讨论中体现的几何哲学,使得他证明平行公设时回避了困扰前人的几何直观.他在同时期的数学工作中将圆函数和双曲函数类比,反映出其虚半径球面类比思想的来源和应用.
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| 关 键 词： | 兰伯特 平行线理论 锐角假设 虚半径球面 非欧几何 |
On Lambert's Geometrical Thoughts |
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| GUO Chan-chan.On Lambert's Geometrical Thoughts[J].Studies In Dialectics of Nature,2022(1):83-89. |
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| Authors: | GUO Chan-chan |
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| Affiliation: | (School of Mathematics and Computer Science,Yan’an University,Yan'an 716000,China) |
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| Abstract: | German mathematician Lambert proposed that the hypothesis of acute is established on the imaginary radius sphere.This idea,which plays a crucial role in the establishment and development of non-Euclidean geometry,was on the analogy of sphere.Lambert’s geometrical philosophy embodied in the discussion of axioms and definitions made him avoid the geometric intuition that plagued his predecessors when he proved the parallel postulate.His analogy thought between the circular function and the hyperbolic function in his cotemporaneous mathematics work,reflecting the origin and application of the analogy thought of the imaginary sphere. |
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| Keywords: | Lambert theory of parallel lines hypothesis of acute angle imaginary sphere non-Euclidean geometry |
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