2010华罗庚班刊物-奇点.pdf

目录


由“量头围订制军训帽”引发的对等价变换思想的思考„„„„„„„„„„汤国志 1
浅谈极限的历史„„„„„„„„„„„„„„„„„„„„„„„„„„„李佳宝 4
“等价变换”在数学中的应用实例与研究„„„„„„„„„„„„„„„„刘松涛 6
序列极限求解方法探究关于极限的思想、例证及探究„„„„„„„„„„„杜昊 8
从数列极限到函数极限„„„„„„„„„„„„„„„„„„„„„„„„王梦仑 10
数学计算中等价变换的研究„„„„„„„„„„„„„„„„„„„„„„陈安琪 12
数学中的数形结合思想例证及研究„„„„„„„„„„„„„„„„„„„王宗继 14
等价转换思想的具体应用„„„„„„„„„„„„„„„„„„„„„„„洪浩然 16
数学中的数形结合思想例证及研究„„„„„„„„„„„„„„„„„„„钱源 19
定性与半定量分析„„„„„„„„„„„„„„„„„„„„„„„„„„冯向南 20
数学中的美(浅谈数学中“数形结合”思想例证及研究)„„„„„„„„„段潇楠 21
“等价变换”思想例证及研究„„„„„„„„„„„„„„„„„„„„„包含 25
无限趋近—数学中“极限”思发想例证及研究„„„„„„„„„„„„„„王居方 27
数学中等价变换思想例证及研究„„„„„„„„„„„„„„„„„„„„苏腾飞 29
关于数形结合的有关思考„„„„„„„„„„„„„„„„„„„„„„„刘冠硕 31
数形结合浅谈„„„„„„„„„„„„„„„„„„„„„„„„„„„„王天宇 33
第 1 卷第 1 期奇点 Vol. 1 No. 1
2010 年 11 月 Journal of Singularity November 2010

由“量头围订制军训帽”引发的对等价变换思想的思考

汤国志

北京航空航天大学数学与系统科学学院华罗庚班北京 102206

摘要:基于生活中的一个简单测量问题,引发的对等价变换思想的思考。本文以一些为人们熟知的故事,结合一些简单例
题,说明等价变换思想的作用及其在方程和解析几何问题中的应用。
关键词:等价变换,方程,解析几何问题
A Thought of equivalence es from “Measure head
circumference to bespeak hat of military training”
TANG GUOZHI
(School of Mathematics and Systems Science, Beihang University, HLG Class Beijing 102206, China)
Abstract: This article introduce a thought of equivalence transformation based on a simple measurement problem in our
to some famous stories and simple examples,we can see the function of equivalence transformation and its
applications in equations and Problem of Analytic Geometry.
Keywords: equivalence transformation; equation; problem of analytic geometry.






0 引言 M
了白银。即, 若工匠加了银,体积一定
V Au Ag
那一日在图书馆自修,忽接到班长的短信:“速速报
有变化。
上头围,订制军训帽子!”出于对自己脑袋高度负责的态
当时没有成份分析等一些高端技术,若从成份来考察,
度,我决定实测一下,可是当时身边只有不容毁坏的神圣
当时的工具不可能完成任务,但阿基米德巧妙地将这一问题
课本以及一把钢板尺,要怎么测呢?思索了一会儿之后,
变换到考察体积的方面,完成了体积比较,便也等价于完成
我想到了自己的耳机线,可以用耳机线围绕头一周,再测
了成份的检验。
耳机线的直线长度,不就可以完成任务了吗!由这种方法,
便将用钢板尺不可能完成,或者是完成了误差会较大的任
务,转化为曲线围绕、变曲为直、测直线长度的任务,大 2 爱迪生测量灯泡容积
大降低了测量误差,完成了任务。爱迪生在发明灯泡的过程中,一次要求其助手测灯泡容
简