本文選題：高斯絕妙定理　切入點(diǎn)：高斯曲率　出處：《自然辯證法研究》2017年09期

【摘要】：現(xiàn)代微分幾何學(xué)與古典微分幾何學(xué)的重要區(qū)別在于前者關(guān)注內(nèi)蘊(yùn)的幾何對象以及內(nèi)蘊(yùn)的幾何性質(zhì)。帶來這一歷史轉(zhuǎn)折的是高斯絕妙定理,高斯所發(fā)現(xiàn)和證明的絕妙定理使得高斯關(guān)注曲面的內(nèi)蘊(yùn)性質(zhì),并進(jìn)而導(dǎo)致內(nèi)蘊(yùn)幾何學(xué)的建立。高斯建立絕妙定理的過程是高斯內(nèi)蘊(yùn)幾何學(xué)起源的最重要線索。但目前關(guān)于絕妙定理建立過程的歷史研究,最多給出高斯相關(guān)工作的年譜。在研究原始文獻(xiàn)和相關(guān)研究文獻(xiàn)基礎(chǔ)上,梳理高斯關(guān)于絕妙定理相關(guān)工作之間的歷史關(guān)聯(lián),還原高斯發(fā)現(xiàn)和證明絕妙定理的過程,提出并回答關(guān)于絕妙定理的幾個(gè)歷史問題。
[Abstract]:The important difference between modern differential geometry and classical differential geometry is that the former pays close attention to the geometric object of connotation and the geometric nature of connotation. The wonderful theorem discovered and proved by Gao Si made Gao Si pay attention to the intrinsic properties of the surface. And then lead to the establishment of intrinsic geometry. Gao Si's process of establishing wonderful theorems is the most important clue to the origin of Gao Si's intrinsic geometry. At most, the chronology of Gao Si's related work is given. On the basis of studying the original literature and related research documents, this paper combs the historical correlation between the relevant work of Gao Si's work on the excellent theorem, and restores the process of discovering and proving the brilliant theorem in Gao Si. Several historical questions about the excellent theorem are put forward and answered.
【作者單位】： 西北大學(xué)科學(xué)史高等研究院;
【基金】：國家自然科學(xué)基金資助項(xiàng)目“從Gauss到Riemann的微分幾何學(xué)之歷史研究”(1166010148);“代數(shù)方程之Galois理論的若干歷史問題研究”(11571276)
【分類號】：O186.1
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本文編號：1688369