複數與幾何
摘要
複數是中學代數課程中數的概念最後1次擴展.初學複數時,對它的存在往往會感到懷疑,認爲它是虛無縹緲的數.事實上,複數的應用非常廣泛,特別是在幾何中的應用.本文利用複數來研究幾何,主要考慮如下的問題:平面上的點集的複數表示;平面曲線的複數表示;複數在共線、共點、共圓、複數的.麥比烏斯變換等幾何問題上的應用,在說明這些應用的同時介紹1些數學上常用的思考方法.
關鍵詞:複數;複數運算;平面點集;平面曲線;幾何應用;複數方法;麥比烏斯變換
Complex numbers and geometry
ABSTRACT
Complex numbers is the last expansion of numbers’ concept of the algebra course in middle school. While n the complex numbers,people will often feel doubtful to its existence and think it is illusory fact,its applications are very extensive, especially the application in geometry. This thesis makes use of complex numbers to study geometry. It mainly considers the following questions: using complex numbers to express collected points and curves on the level;geometric applications of complex numbers on collinear,concurrent,round,Mobius Mappings of Complex numbers problems,while,this thesis recommends some methods for thinking on mathematics.
Keywords:Complex numbers; Complex numbers operation; Collected points on the level; Curves on the level ; Geometric application; Complex numbers’ methods; Mobius Mappings