对称思想在几何中的应用研究
摘 要
对称思想是一种重要的数学思想，存在于数学的很多领域，我们对其应该给予足够的重视。对称思想是研究数学问题常用的思想方法，对称是一种美， 数学中的对称美主要表现在几何图形的对称、式子的对称、解题方法的对称等方面。本文讨论对称思想在平面几何、解析几何、立体几何、射影几何中的应用并举例说明分析。
关键词 对称思想 几何应用
the Rearch of Symmetrical Idea in the Gemmetry
（School of Mathematical Science，Huaibei Normal University，Huaibei，235000）
Abstract
Symmetrical idea is an important mathematical thought, which exists in many areas of mathematics, of which we should give enough attention. Symmetrical idea is thinking method which is the study math problems commonly ud .Symmetry is a beauty, the symmetrical beauty of mathematics is mainly manifested in the symmet-
rical geometric figure, the symmetrical formula, the symmetrical method of solving problem,ect. This paper discuss symmetrical ideas in plane geometry, and analytic geometry, three-dimensional geometry, projective geometry, and illustrates the appli-
cation.
Key Words: Symmetry idea Geometrical application
引 言··························································1
一 对称思想的意义·················································1
二 几何的对称性···················································1
（一）几何公式的对称性···········································2
（二）几何图形的对称性···········································2
（三）对称的广泛应用·············································2
三 对称思想在初等数学中的应用·····································3
（一）对称思想在平面解析几何中的应用······························3
（二）对称思想在立体几何中的应用··································11
四 对称思想在高等数学中的应用····································12
（一）对称思想在射影几何中的应用·································12
（二）对称思想在微分学中的应用···································15
（三）对称思想在积分学中的应用···································16
五 对称思想的进一步探讨··········································18
