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空间解析几何产生于18世纪前半叶,较平面解析几何约晚一个世纪。由于有平面解析几何研究图形与方程的思想基础,所以在克雷洛和拉盖尔建立了空间直角坐标系后,空间解析几何的传统内容就很快完成了。到了19世纪后期,向量代数理论也完成了。虽然在这之前,向量知识就经常用在力学上,但还是到了20世纪初期,向量代数才完全进入空间解析几何而变成了它的组成部分。这是空间解析几何的一次大改革。因为它运用了先进的工具,使空间图形的研究得到了很大的方便。其后解析几何又向高维空间发展,从而产生了汛函分析和代数几何。这些都说明一个古老的数学分支——解析几何学是在不断地更新换代的。
Spatial analytic geometry originated in the first half of the 18th century, about a century later than plane-resolved geometry. Because of the ideological foundations of graphs and equations for plane-resolved geometry, the traditional content of spatial analytic geometry was quickly completed after Creole and Laguerre established the Cartesian coordinate system. By the late 19th century, vector algebra theory was completed. Although prior knowledge of vectors was often used in mechanics, it was not until early in the twentieth century that vector algebra became part of it by moving completely into spatial analytic geometry. This is a major reform of spatial analytic geometry. Because of its use of advanced tools, the study of spatial graphics has been greatly facilitated. Later, analytic geometry developed to high-dimensional space again, resulting in flood analysis and algebraic geometry. All of this shows that an ancient branch of mathematics - analytic geometry is constantly being replaced.