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本文的主題同时涉及代数和几何,这两門学科間的联系是很多种多样的,而且对它們的每一門来說都是有益的。代数在几何和几何在代数中的很多应用,在远古时代就已經知道了。这只要回顾关于根据把边为(a+b)的正方形分解为两个小的正方形和两个长方形的公式(a+b)~2=a~2+2ab+b~2的結論,或者关于用代数方法来解作图題就够了。晚近,甚至在这个世紀,在数学里面出現了很多和代数及几何同样有关的研究方向;可以作为很好的例子的,有代数几何以及在活跃发展中的方向——它因为沒有較好的名称,暫且叫作“綫性代数和投影几何”。在代数的范围內,已經产生的关于复数的学說,很多地方都与几何有联系;本文将只談这些联系中的一个。
The subject of this article covers both algebra and geometry. The links between the two disciplines are very diverse and beneficial to each of them. Many applications of algebra in algebra in geometry and geometry have been known since ancient times. This only goes back to the conclusion of the formula (a+b)~2=a~2+2ab+b~2 based on the decomposition of the square whose side is (a+b) into two small squares and two rectangles, or about It is enough to solve the drawing problem with algebraic methods. Lately, even in this century, there have been many research directions in mathematics that are equally relevant to algebra and geometry; as a good example, there is algebraic geometry and the direction in active development - because it does not have a good name For the time being, it is called “linear algebra and projection geometry.” In the context of algebra, the doctrines concerning complex numbers that have been produced are in many places related to geometry; this article will only discuss one of these connections.