扫一扫
关注中图网
官方微博
本类五星书更多>
-
>
宇宙、量子和人类心灵
-
>
气候文明史
-
>
南极100天
-
>
考研数学专题练1200题
-
>
希格斯:“上帝粒子”的发明与发现
-
>
神农架叠层石:10多亿年前远古海洋微生物建造的大堡礁
-
>
声音简史
神奇的几何辅助线 版权信息
- ISBN：9787121452833
- 条形码：9787121452833 ; 978-7-121-45283-3
- 装帧：平装-胶订
- 册数：暂无
- 重量：暂无
- 所属分类：>
神奇的几何辅助线 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*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。
神奇的几何辅助线 目录
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
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
展开全部
神奇的几何辅助线 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.
书友推荐
- >
经典常谈
经典常谈
¥16.7¥39.8 - >
龙榆生：词曲概论/大家小书
龙榆生：词曲概论/大家小书
¥8.7¥24.0 - >
莉莉和章鱼
莉莉和章鱼
¥14.4¥42.0 - >
诗经-先民的歌唱
诗经-先民的歌唱
¥14.5¥39.8 - >
伊索寓言-世界文学名著典藏-全译本
伊索寓言-世界文学名著典藏-全译本
¥6.7¥19.0 - >
名家带你读鲁迅:故事新编
名家带你读鲁迅:故事新编
¥13.0¥26.0 - >
企鹅口袋书系列·伟大的思想20:论自然选择(英汉双语)
企鹅口袋书系列·伟大的思想20:论自然选择(英汉双语)
¥6.3¥14.0 - >
人文阅读与收藏·良友文学丛书:一天的工作
人文阅读与收藏·良友文学丛书:一天的工作
¥15.7¥45.8
本类畅销
-
数学的魅力;初等数学概念演绎
¥9.4¥22 -
普林斯顿微积分读本-(修订版)
¥62.4¥99 -
高等几何
¥8.8¥20 -
离散数学(第六版)
¥43.4¥49.9 -
偏微分方程
¥20.9¥33.7 -
数学·统计学系列二维.三维欧式几何的对偶原理
¥96.6¥138
浏览历史
中高温传热蓄热材料
¥85.0¥118.0概率论与数理统计(第2版)
¥26.9¥39.8妈妈超有想象力——陪你一起等风
¥14.6¥20.0黄河水沙实体模拟设计理论及应用
¥135.0¥180.0中学几何专题研究
¥31.3¥55.0
