平面几何32讲

作者: 周春荔

出版社: 电子工业出版社

出版时间: 2023-02

版次: 1

ISBN: 9787121449512

定价: 96.80

装帧: 其他

页数: 368页

分类: 自然科学

8人买过

本书内容与初中、高中数学新编数学教材同步配套，把初中、高中数学中涉及到的全部平面几何知识整合梳理到本书中，全书分为32讲，每讲都有基本知识讲解，以及精选典型例题讲解，作者为了能发散读者数学思维，培养读者平面几何学习兴趣，很多题目都进行了一题多解。本书是由作者多年给全国各地的学校做讲座的内容改编而成的，内容经典、丰富、有趣，内容循序渐进，能满足不同读者的不同需求。想要梳理平面几何知识的学生以及对平面几何感兴趣的读者可阅读此书。周春荔，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，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 1 讲线段与角的推理计算························································.1

1.1 基础知识······································································.1

1.2 典型例题精析································································.2

第 2 讲平行线与相交线推理························································.8

2.1 基础知识······································································.8

2.2 典型例题精析································································.9

第 3 讲线段的性质····································································16

3.1 基础知识······································································16

3.2 三角形不等式的简单应用·················································17

3.3 简单的不等式与极值·······················································20

第 4 讲三角形内角和问题···························································26

4.1 基本知识······································································26

4.2 三角形角的一些性质·······················································26

4.3 有关角的一些计算问题····················································28

4.4 综合竞赛题选析·····························································31

第 5 讲等积变形与面积计算························································37

第 6 讲三角形全等····································································48

6.1 三角形全等的基本例题····················································49

6.2 三角形全等的综合例题····················································52

第 7 讲勾股定理及其应用···························································57

7.1 勾股定理及其逆定理·······················································57

7.2 勾股定理的各种应用·······················································59

第 8 讲三角形中位线定理应用·····················································67

8.1 基础知识······································································67

8.2 基本例题······································································68

8.3 综合例题······································································71

第 9 讲等腰三角形问题······························································76

9.1 基础知识······································································76

9.2 基本证明练习题·····························································78

9.3 竞赛题选讲···································································82

第 10 讲正三角形综合练习 ·························································86

第 11 讲平行四边形的判定与性质 ················································97

第 12 讲梯形的判定与中位线定理 ·············································.108

第 13 讲正方形问题 ·······························································.118

第 14 讲四边形中的趣味竞赛题 ················································.128

第 15 讲平行截割定理 ····························································.140

第 16 讲相似三角形及其应用 ···················································.151

16.1 相似三角形的判定 ·····················································.151

16.2 相似三角形的性质 ·····················································.151

16.3 直角三角形的射影定理 ···············································.151

第 17 讲圆的基本问题 ····························································.166

17.1 圆的基本问题 ···························································.166

17.2 垂径定理及其应用 ·····················································.168

17.3 和圆有关的角及其应用 ···············································.172

第 18 讲四点共圆及其应用 ······················································.181

18.1 四点共圆的基本竞赛题 ···············································.181

18.2 四点共圆的综合应用 ··················································.187

第 19 讲直线与圆 ··································································.194

第 20 讲圆幂定理 ··································································.203

第 21 讲正多边形与圆 ····························································.210

第 22 讲几何图形不等式问题 ···················································.221

第 23 讲几何极值问题 ····························································.238

第 24 讲等积变形与面积证题 ···················································.255

第 25 讲梅涅劳斯定理及其应用 ················································.273

第 26 讲塞瓦定理及其应用 ······························
内容简介:
本书内容与初中、高中数学新编数学教材同步配套，把初中、高中数学中涉及到的全部平面几何知识整合梳理到本书中，全书分为32讲，每讲都有基本知识讲解，以及精选典型例题讲解，作者为了能发散读者数学思维，培养读者平面几何学习兴趣，很多题目都进行了一题多解。本书是由作者多年给全国各地的学校做讲座的内容改编而成的，内容经典、丰富、有趣，内容循序渐进，能满足不同读者的不同需求。想要梳理平面几何知识的学生以及对平面几何感兴趣的读者可阅读此书。
作者简介:
周春荔，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，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 1 讲线段与角的推理计算························································.1

1.1 基础知识······································································.1

1.2 典型例题精析································································.2

第 2 讲平行线与相交线推理························································.8

2.1 基础知识······································································.8

2.2 典型例题精析································································.9

第 3 讲线段的性质····································································16

3.1 基础知识······································································16

3.2 三角形不等式的简单应用·················································17

3.3 简单的不等式与极值·······················································20

第 4 讲三角形内角和问题···························································26

4.1 基本知识······································································26

4.2 三角形角的一些性质·······················································26

4.3 有关角的一些计算问题····················································28

4.4 综合竞赛题选析·····························································31

第 5 讲等积变形与面积计算························································37

第 6 讲三角形全等····································································48

6.1 三角形全等的基本例题····················································49

6.2 三角形全等的综合例题····················································52

第 7 讲勾股定理及其应用···························································57

7.1 勾股定理及其逆定理·······················································57

7.2 勾股定理的各种应用·······················································59

第 8 讲三角形中位线定理应用·····················································67

8.1 基础知识······································································67

8.2 基本例题······································································68

8.3 综合例题······································································71

第 9 讲等腰三角形问题······························································76

9.1 基础知识······································································76

9.2 基本证明练习题·····························································78

9.3 竞赛题选讲···································································82

第 10 讲正三角形综合练习 ·························································86

第 11 讲平行四边形的判定与性质 ················································97

第 12 讲梯形的判定与中位线定理 ·············································.108

第 13 讲正方形问题 ·······························································.118

第 14 讲四边形中的趣味竞赛题 ················································.128

第 15 讲平行截割定理 ····························································.140

第 16 讲相似三角形及其应用 ···················································.151

16.1 相似三角形的判定 ·····················································.151

16.2 相似三角形的性质 ·····················································.151

16.3 直角三角形的射影定理 ···············································.151

第 17 讲圆的基本问题 ····························································.166

17.1 圆的基本问题 ···························································.166

17.2 垂径定理及其应用 ·····················································.168

17.3 和圆有关的角及其应用 ···············································.172

第 18 讲四点共圆及其应用 ······················································.181

18.1 四点共圆的基本竞赛题 ···············································.181

18.2 四点共圆的综合应用 ··················································.187

第 19 讲直线与圆 ··································································.194

第 20 讲圆幂定理 ··································································.203

第 21 讲正多边形与圆 ····························································.210

第 22 讲几何图形不等式问题 ···················································.221

第 23 讲几何极值问题 ····························································.238

第 24 讲等积变形与面积证题 ···················································.255

第 25 讲梅涅劳斯定理及其应用 ················································.273

第 26 讲塞瓦定理及其应用 ······························

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平面几何32讲

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作者简介:

目录: