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神奇的幾何輔助線 版權信息
- ISBN：9787121452833
- 條形碼：9787121452833 ; 978-7-121-45283-3
- 裝幀：平裝-膠訂
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
神奇的幾何輔助線 內容簡介
本書集周春荔教授畢生所學，將幾何輔助線的添加方法和原理娓娓道來，充分體現"數學是智力的磨刀石，對于所有信奉教育的人而言，是一種不可缺少的思維訓練”的育人作用。幾何定理的證明，除少數簡易的以外，非添加有用的輔助線，否則就無從著手。輔助線的作法，千變萬化，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、方法和建構講得如此清晰明了，學生系統學習后，會得心應手解決幾何相關問題。
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 分析數學題的思路 ·····························································.11
1.2.1 倒推分析思路 ··························································.11
1.2.2 分析綜合思路 ··························································.13
1.2.3 反設分析思路 ··························································.15
1.3 幾種數學解題探索方法 ·······················································.17
1.3.1 試驗發現法 ·····························································.17
1.3.2 聯想類比法 ·····························································.18
1.3.3 反例證偽法 ·····························································.19
1.3.4 數形結合的構造圖形法 ···············································.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 作圖構造 ·····························································.33
原則四 顯現特殊性 ··························································.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 構造圓進行添加輔助線 ···············································.80
2.4.8 利用復合變換添加輔助線 ············································.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 例說構造圖形解題 ···························································.141
3.1 構造圖形解幾何題 ···························································.143
3.2 構造圖形解三角題 ···························································.153
3.3 構造圖形解代數題 ···························································.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 分析數學題的思路 ·····························································.11
1.2.1 倒推分析思路 ··························································.11
1.2.2 分析綜合思路 ··························································.13
1.2.3 反設分析思路 ··························································.15
1.3 幾種數學解題探索方法 ·······················································.17
1.3.1 試驗發現法 ·····························································.17
1.3.2 聯想類比法 ·····························································.18
1.3.3 反例證偽法 ·····························································.19
1.3.4 數形結合的構造圖形法 ···············································.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 作圖構造 ·····························································.33
原則四 顯現特殊性 ··························································.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 構造圓進行添加輔助線 ···············································.80
2.4.8 利用復合變換添加輔助線 ············································.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 例說構造圖形解題 ···························································.141
3.1 構造圖形解幾何題 ···························································.143
3.2 構造圖形解三角題 ···························································.153
3.3 構造圖形解代數題 ···························································.162
展開全部
神奇的幾何輔助線 作者簡介
周春荔，中國數學會會員，中國數學奧林匹克首批高級教練員。數學科學方法論研究交流中心副主任。曾任首都師范大學數學系數學教育教研室主任，《數學教育學報》編委，華羅庚金杯少年數學邀請賽主試委員會副主任。一直從事初等數學與數學教育、數學方法論與數學思想史、奧林匹克數學的綜合研究與教學，有著豐富的競賽選手及教練員培訓的經驗，發表過多部數學競賽方面的著作與論文，主編或參編過許多適合中小學數學愛好者使用的教程、讀本或資料，參加過多種競賽的命題工作。北京數學奧林匹克學校的創始人之一，首任副校長，長期擔任北京數學會普及工作委員會副主任，授課深入淺出，富有啟發性.所寫的數學普及讀物和生動有趣的課堂教學很受青少年數學愛好者的歡迎.
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