本文在介绍对称性的研究背景、研究意义后给出了对称性的相关概念及其性质并利用对称性及其性质讨论了中学数学中的平面几何、方程、函数的相关问题以及高等数学中的行列式、求导、积分的相关问题发现在与对称性相关的问题时如果能充分考虑到对称性的因素利用对称性解题可以起到化繁为简、化难为易的效果翻译这段话

This article introduces the research background and significance of symmetry, and presents the relevant concepts and properties of symmetry. Using symmetry and its properties, we discuss the related problems in plane geometry, equations, and functions in secondary school mathematics, as well as the related problems in determinants, derivatives, and integrals in advanced mathematics. It is found that when dealing with problems related to symmetry, if the factors of symmetry can be fully considered and utilized for problem-solving, it can simplify and facilitate the process