从双曲线到双曲面的若干性质推广.pdfVIP

本科生毕业论文 （设计） 题目：从双曲线到双曲面的若干性质推广 学 院 数学与统计学院 学科门类 理 学 专 业 数学与应用数学 学 号 1207410079 姓 名 杭文伍 指导教师 汪小玉 2016年 4 月 15 日 合肥师范学院2016届本科生毕业论文 （设计） 摘 要 双曲线和双曲面在实际生活中有着十分广泛的应用，特别是在建筑工程和器械工程的 应用中，它们起起到了决定这个项目成功与否.双曲线和双曲面是解析几何研究的重要内 容，也是数学的一条十分重要的分支.双曲线是中学所学的课程，也是大学解析几何所要 掌握的重要内容.双曲面是大学本科生所要学习的内容.二者之间有许多联系和相似的性 质，而我们在大学本科课程的学习中并没有学习它们的性质之间的关系，我们只是分开地 学习它们，并没有将二者联系起来加以研究.因此本文通过对双曲线和双曲面的有关性质 的梳理，并试图找出二者的性质之间的联系.也就是说，把双曲线的某些性质推广到双曲 线中来.通过对这些性质的推广与研究来了解双曲线和双曲面的性质的异同，并为日后的 科研或者工作生活做铺垫. 关键词：双曲线；双曲面；性质；推广 abstract Hyperbolicandhyperboloid in real lifehasaverywiderangeofapplications, especially intheconstructionengineeringandequipmentengineeringapplications, play a decision on thisproject a success.Hyperbolic hyperboloid isan important part of the study of analytic geometry, and is also a very important branch of mathematics. Hyperbola is learning courses in middle school, and university to master the important content of analytic geometry. Hyperboloid is to learn the contents of university students. There are a lot of contact between them and the similarproperties,andwe inuniversityundergraduatecourseofstudyandnostudy of the relationship between their properties, we just learn them separately, and there is no link between study. This article through to the hyperbolic and hyperboloid about the nature of the comb, and trying to find out the nature of the relationship between. That is to say, some properties of the hyperbolic to hyperbola. Through the study on the nature of the promotion and to understand the nature of the hyperbola and hyperboloid of the similarities and differences, and groundwork for future scientific research or work life. Key words:Hyperbolic;Hyperboloid. Proper