神奇的几何辅助线

作者: 周春荔

出版社: 电子工业出版社

出版时间: 2023-03

版次: 1

ISBN: 9787121452833

定价: 49.80

装帧: 其他

页数: 196页

分类: 自然科学

11人买过

本书集周春荔教授毕生所学，将几何辅助线的添加方法和原理娓娓道来，充分体现\"数学是智力的磨刀石，对于所有信奉教育的人而言，是一种不可缺少的思维训练”的育人作用。几何定理的证明，除少数简易的以外，非添加有用的辅助线，否则就无从着手。辅助线的作法，千变万化，没有一定的方法可以遵循，所以是证题时最困难的一件事。在普通几何书中，很少有将几何辅助线的原理、方法和建构讲得如此清晰明了，学生系统学习后，会得心应手解决几何相关问题。周春荔，中国数学会会员，中国数学奥林匹克首批高级教练员。数学科学方法论研究交流中心副主任。曾任首都师范大学数学系数学教育教研室主任，《数学教育学报》编委，华罗庚金杯少年数学邀请赛主试委员会副主任。一直从事初等数学与数学教育、数学方法论与数学思想史、奥林匹克数学的综合研究与教学，有着丰富的竞赛选手及教练员培训的经验，发表过多部数学竞赛方面的著作与论文，主编或参编过许多适合中小学数学爱好者使用的教程、读本或资料，参加过多种竞赛的命题工作。北京数学奥林匹克学校的创始人之一，首任副校长，长期担任北京数学会普及工作委员会副主任，授课深入浅出，富有启发性.所写的数学普及读物和生动有趣的课堂教学很受青少年数学爱好者的欢迎. 第一章几何证题知识概述 ······························································.1

1.1 命题的四种形式与充分必要条件 ············································.2

1.1.1 命题的四种形式 ························································.2

1.1.2 充分条件与必要条件 ···················································.4

1.2 分析数学题的思路 ·····························································.11

1.2.1 倒推分析思路 ··························································.11

1.2.2 分析综合思路 ··························································.13

1.2.3 反设分析思路 ··························································.15

1.3 几种数学解题探索方法 ·······················································.17

1.3.1 试验发现法 ·····························································.17

1.3.2 联想类比法 ·····························································.18

1.3.3 反例证伪法 ·····························································.19

1.3.4 数形结合的构造图形法 ···············································.19

第二章神奇的几何辅助线 ·····························································.25

2.1 添加辅助线的目的 ·····························································.25

2.2 添加辅助线的原则 ·····························································.30

原则一化繁为简 ·····························································.30

原则二相对集中 ·····························································.31

原则三作图构造 ·····························································.33

原则四显现特殊性 ··························································.34

2.3 名题剖析智慧精华 ·····························································.35

2.4 图形变换与辅助线 ·····························································.38

2.4.1 应用平移变换添加辅助线 ············································.39

2.4.2 反射变换添加辅助线作法 ············································.50

2.4.3 通过旋转变换添加辅助线的作用 ···································.63

2.4.4 利用中心对称添加辅助线 ············································.73

2.4.5 利用相似变换添加辅助线 ············································.76

2.4.6 利用等积变换添加辅助线 ············································.78

2.4.7 构造圆进行添加辅助线 ···············································.80

2.4.8 利用复合变换添加辅助线 ············································.88

2.5 综合示范添加辅助线解题 ····················································.90

2.5.1 经典例题添加辅助线赏析 ············································.91

2.5.2 著名竞赛题添加辅助线选析 ·······································.109

2.5.3 一题多证添加辅助线例谈 ··········································.132

第三章例说构造图形解题 ···························································.141

3.1 构造图形解几何题 ···························································.143

3.2 构造图形解三角题 ···························································.153

3.3 构造图形解代数题 ···························································.162
内容简介:
本书集周春荔教授毕生所学，将几何辅助线的添加方法和原理娓娓道来，充分体现\"数学是智力的磨刀石，对于所有信奉教育的人而言，是一种不可缺少的思维训练”的育人作用。几何定理的证明，除少数简易的以外，非添加有用的辅助线，否则就无从着手。辅助线的作法，千变万化，没有一定的方法可以遵循，所以是证题时最困难的一件事。在普通几何书中，很少有将几何辅助线的原理、方法和建构讲得如此清晰明了，学生系统学习后，会得心应手解决几何相关问题。
作者简介:
周春荔，中国数学会会员，中国数学奥林匹克首批高级教练员。数学科学方法论研究交流中心副主任。曾任首都师范大学数学系数学教育教研室主任，《数学教育学报》编委，华罗庚金杯少年数学邀请赛主试委员会副主任。一直从事初等数学与数学教育、数学方法论与数学思想史、奥林匹克数学的综合研究与教学，有着丰富的竞赛选手及教练员培训的经验，发表过多部数学竞赛方面的著作与论文，主编或参编过许多适合中小学数学爱好者使用的教程、读本或资料，参加过多种竞赛的命题工作。北京数学奥林匹克学校的创始人之一，首任副校长，长期担任北京数学会普及工作委员会副主任，授课深入浅出，富有启发性.所写的数学普及读物和生动有趣的课堂教学很受青少年数学爱好者的欢迎.
目录:
第一章几何证题知识概述 ······························································.1

1.1 命题的四种形式与充分必要条件 ············································.2

1.1.1 命题的四种形式 ························································.2

1.1.2 充分条件与必要条件 ···················································.4

1.2 分析数学题的思路 ·····························································.11

1.2.1 倒推分析思路 ··························································.11

1.2.2 分析综合思路 ··························································.13

1.2.3 反设分析思路 ··························································.15

1.3 几种数学解题探索方法 ·······················································.17

1.3.1 试验发现法 ·····························································.17

1.3.2 联想类比法 ·····························································.18

1.3.3 反例证伪法 ·····························································.19

1.3.4 数形结合的构造图形法 ···············································.19

第二章神奇的几何辅助线 ·····························································.25

2.1 添加辅助线的目的 ·····························································.25

2.2 添加辅助线的原则 ·····························································.30

原则一化繁为简 ·····························································.30

原则二相对集中 ·····························································.31

原则三作图构造 ·····························································.33

原则四显现特殊性 ··························································.34

2.3 名题剖析智慧精华 ·····························································.35

2.4 图形变换与辅助线 ·····························································.38

2.4.1 应用平移变换添加辅助线 ············································.39

2.4.2 反射变换添加辅助线作法 ············································.50

2.4.3 通过旋转变换添加辅助线的作用 ···································.63

2.4.4 利用中心对称添加辅助线 ············································.73

2.4.5 利用相似变换添加辅助线 ············································.76

2.4.6 利用等积变换添加辅助线 ············································.78

2.4.7 构造圆进行添加辅助线 ···············································.80

2.4.8 利用复合变换添加辅助线 ············································.88

2.5 综合示范添加辅助线解题 ····················································.90

2.5.1 经典例题添加辅助线赏析 ············································.91

2.5.2 著名竞赛题添加辅助线选析 ·······································.109

2.5.3 一题多证添加辅助线例谈 ··········································.132

第三章例说构造图形解题 ···························································.141

3.1 构造图形解几何题 ···························································.143

3.2 构造图形解三角题 ···························································.153

3.3 构造图形解代数题 ···························································.162

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神奇的几何辅助线

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