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神奇的幾何輔助線 版權(quán)信息
- ISBN：9787121452833
- 條形碼：9787121452833 ; 978-7-121-45283-3
- 裝幀：平裝-膠訂
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>
神奇的幾何輔助線 內(nèi)容簡介
本書集周春荔教授畢生所學(xué)，將幾何輔助線的添加方法和原理娓娓道來，充分體現(xiàn)"數(shù)學(xué)是智力的磨刀石，對于所有信奉教育的人而言，是一種不可缺少的思維訓(xùn)練”的育人作用。幾何定理的證明，除少數(shù)簡易的以外，非添加有用的輔助線，否則就無從著手。輔助線的作法，千變?nèi)f化，沒有一定的方法可以遵循，所以是證題時*困難的一件事。在普通幾何書中，很少有將幾何輔助線的原理、方法和建構(gòu)講得如此清晰明了，學(xué)生系統(tǒng)學(xué)習(xí)后，會得心應(yīng)手解決幾何相關(guān)問題。
神奇的幾何輔助線 目錄
章 幾何證題知識概述 ······························································.1
1.1 命題的四種形式與充分必要條件 ············································.2
1.1.1 命題的四種形式 ························································.2
1.1.2 充分條件與必要條件 ···················································.4
1.2 分析數(shù)學(xué)題的思路 ·····························································.11
1.2.1 倒推分析思路 ··························································.11
1.2.2 分析綜合思路 ··························································.13
1.2.3 反設(shè)分析思路 ··························································.15
1.3 幾種數(shù)學(xué)解題探索方法 ·······················································.17
1.3.1 試驗發(fā)現(xiàn)法 ·····························································.17
1.3.2 聯(lián)想類比法 ·····························································.18
1.3.3 反例證偽法 ·····························································.19
1.3.4 數(shù)形結(jié)合的構(gòu)造圖形法 ···············································.19
第二章 神奇的幾何輔助線 ·····························································.25
2.1 添加輔助線的目的 ·····························································.25
2.2 添加輔助線的原則 ·····························································.30
原則一 化繁為簡 ·····························································.30
原則二 相對集中 ·····························································.31
原則三 作圖構(gòu)造 ·····························································.33
原則四 顯現(xiàn)特殊性 ··························································.34
2.3 名題剖析智慧精華 ·····························································.35
2.4 圖形變換與輔助線 ·····························································.38
2.4.1 應(yīng)用平移變換添加輔助線 ············································.39
2.4.2 反射變換添加輔助線作法 ············································.50
2.4.3 通過旋轉(zhuǎn)變換添加輔助線的作用 ···································.63
2.4.4 利用中心對稱添加輔助線 ············································.73
2.4.5 利用相似變換添加輔助線 ············································.76
2.4.6 利用等積變換添加輔助線 ············································.78
2.4.7 構(gòu)造圓進行添加輔助線 ···············································.80
2.4.8 利用復(fù)合變換添加輔助線 ············································.88
2.5 綜合示范添加輔助線解題 ····················································.90
2.5.1 經(jīng)典例題添加輔助線賞析 ············································.91
2.5.2 著名競賽題添加輔助線選析 ·······································.109
2.5.3 一題多證添加輔助線例談 ··········································.132
第三章 例說構(gòu)造圖形解題 ···························································.141
3.1 構(gòu)造圖形解幾何題 ···························································.143
3.2 構(gòu)造圖形解三角題 ···························································.153
3.3 構(gòu)造圖形解代數(shù)題 ···························································.162
1.1 命題的四種形式與充分必要條件 ············································.2
1.1.1 命題的四種形式 ························································.2
1.1.2 充分條件與必要條件 ···················································.4
1.2 分析數(shù)學(xué)題的思路 ·····························································.11
1.2.1 倒推分析思路 ··························································.11
1.2.2 分析綜合思路 ··························································.13
1.2.3 反設(shè)分析思路 ··························································.15
1.3 幾種數(shù)學(xué)解題探索方法 ·······················································.17
1.3.1 試驗發(fā)現(xiàn)法 ·····························································.17
1.3.2 聯(lián)想類比法 ·····························································.18
1.3.3 反例證偽法 ·····························································.19
1.3.4 數(shù)形結(jié)合的構(gòu)造圖形法 ···············································.19
第二章 神奇的幾何輔助線 ·····························································.25
2.1 添加輔助線的目的 ·····························································.25
2.2 添加輔助線的原則 ·····························································.30
原則一 化繁為簡 ·····························································.30
原則二 相對集中 ·····························································.31
原則三 作圖構(gòu)造 ·····························································.33
原則四 顯現(xiàn)特殊性 ··························································.34
2.3 名題剖析智慧精華 ·····························································.35
2.4 圖形變換與輔助線 ·····························································.38
2.4.1 應(yīng)用平移變換添加輔助線 ············································.39
2.4.2 反射變換添加輔助線作法 ············································.50
2.4.3 通過旋轉(zhuǎn)變換添加輔助線的作用 ···································.63
2.4.4 利用中心對稱添加輔助線 ············································.73
2.4.5 利用相似變換添加輔助線 ············································.76
2.4.6 利用等積變換添加輔助線 ············································.78
2.4.7 構(gòu)造圓進行添加輔助線 ···············································.80
2.4.8 利用復(fù)合變換添加輔助線 ············································.88
2.5 綜合示范添加輔助線解題 ····················································.90
2.5.1 經(jīng)典例題添加輔助線賞析 ············································.91
2.5.2 著名競賽題添加輔助線選析 ·······································.109
2.5.3 一題多證添加輔助線例談 ··········································.132
第三章 例說構(gòu)造圖形解題 ···························································.141
3.1 構(gòu)造圖形解幾何題 ···························································.143
3.2 構(gòu)造圖形解三角題 ···························································.153
3.3 構(gòu)造圖形解代數(shù)題 ···························································.162
展開全部
神奇的幾何輔助線 作者簡介
周春荔，中國數(shù)學(xué)會會員，中國數(shù)學(xué)奧林匹克首批高級教練員。數(shù)學(xué)科學(xué)方法論研究交流中心副主任。曾任首都師范大學(xué)數(shù)學(xué)系數(shù)學(xué)教育教研室主任，《數(shù)學(xué)教育學(xué)報》編委，華羅庚金杯少年數(shù)學(xué)邀請賽主試委員會副主任。一直從事初等數(shù)學(xué)與數(shù)學(xué)教育、數(shù)學(xué)方法論與數(shù)學(xué)思想史、奧林匹克數(shù)學(xué)的綜合研究與教學(xué)，有著豐富的競賽選手及教練員培訓(xùn)的經(jīng)驗，發(fā)表過多部數(shù)學(xué)競賽方面的著作與論文，主編或參編過許多適合中小學(xué)數(shù)學(xué)愛好者使用的教程、讀本或資料，參加過多種競賽的命題工作。北京數(shù)學(xué)奧林匹克學(xué)校的創(chuàng)始人之一，首任副校長，長期擔(dān)任北京數(shù)學(xué)會普及工作委員會副主任，授課深入淺出，富有啟發(fā)性.所寫的數(shù)學(xué)普及讀物和生動有趣的課堂教學(xué)很受青少年數(shù)學(xué)愛好者的歡迎.
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