抽屜原理及應(yīng)用


目錄

第一章 抽屜原理……………………………………………………………………1
1.1 抽屜原理的介紹…………………………………………………………………………1
1.2 抽屜原理的常見(jiàn)行式……………………………………………………………………1
1.2.1 抽屜原理的簡(jiǎn)單形式………………………………………………………………1
1.2.2 抽屜原理的一般形式………………………………………………………………1
1.2.3 抽屜原理的加強(qiáng)形式………………………………………………………………1
第二章 抽屜的構(gòu)造方法及例子……………………………………………………2
2.1 分割圖形/區(qū)間構(gòu)造抽屜…………………………………………………………………2
2.2 利用整數(shù)的性質(zhì)分組構(gòu)造抽屜…………………………………………………………3
2.2.1 按整數(shù)分類構(gòu)造抽屜………………………………………………………………3
2.2.2 按余數(shù)分類構(gòu)造抽屜………………………………………………………………3
2.3 以集合構(gòu)造抽屜…………………………………………………………………………4
2.4 轉(zhuǎn)化的的方法構(gòu)造抽屜…………………………………………………………………4
第三章 抽屜原理的應(yīng)用……………………………………………………………5
3.1 利用抽屜原理解題…………………………………………………………………………5
3.1.1利用抽屜原理證明不等式…………………………………………………………5
3.1.4 抽屜原理在幾何中的應(yīng)用………………………………………………………6
3.2 抽屜原理在高等數(shù)學(xué)中應(yīng)用………………………………………………………………7
3.1.1 抽屜原理在無(wú)限集中的應(yīng)用……………………………………………………7
3.1.2 抽屜原理在高等代數(shù)中的應(yīng)用…………………………………………………8
3.1.3 抽屜原理在數(shù)論中的應(yīng)用………………………………………………………9
3.3抽屜原理在生活中的應(yīng)用…………………………………………………………………11
3.2.1 利用抽屜原理解釋生活中的現(xiàn)象………………………………………………11
3.2.2 利用抽屜原理決策………………………………………………………………12
結(jié)論…………………………………………………………………………………13
致謝…………………………………………………………………………………14
參考文獻(xiàn)……………………………………………………………………………15



摘要 抽屜原理是重要的非常規(guī)解題方法之一，主要用于處理存在性問(wèn)題。本文主要以一些例題來(lái)說(shuō)明抽屜原理的特點(diǎn)和應(yīng)用。運(yùn)用抽屜原理的關(guān)鍵是構(gòu)造合適的抽屜和物體，構(gòu)造抽屜的過(guò)程也即物體分類的過(guò)程，首先我們會(huì)介紹幾種常見(jiàn)的構(gòu)造抽屜的方法如分割圖形，整數(shù)分類等。然后運(yùn)用抽屜原理結(jié)合高等數(shù)學(xué)的相關(guān)知識(shí)對(duì)其進(jìn)行拓展，用以解決無(wú)限集合、代數(shù)、數(shù)論和幾何上的一些問(wèn)題。論文的最后針對(duì)現(xiàn)實(shí)生活中的一些事實(shí)基于抽屜原理給出解答，并分析抽屜原理運(yùn)用于生活中需要的注意的地方。

關(guān)鍵詞：抽屜原理 無(wú)限集合 代數(shù) 數(shù)論 幾何


The principle of drawer and its application

Abstract Drawer principle is one of the important unconventional solving methods,which mainly used for proving of existence problem. This paper takes several examples to illustrate the features and application of the drawer principle. The key of applying the principle of drawer is construct a proper drawer and object. In fact,the constructing of drawer is same as object classification.The First,we introduced some common methods of constructing the drawer such as the segmentation graph,integer classification and so on. Then related the drawer principle with the advanced mathematics knowledge for its expand in application,so that it can solve the problem in infinite set ,Algebraic ,Geometry and Number theory. The Finally , answer some of the fact in real life based with the drawer principle and analyze the main points of use of the drawer principle in daily life.

Key words drawer principle infinite set Algebraic Number theory Geometry