神奇的几何辅助线
正版保障 假一赔十 可开发票
￥ 32.87 6.6折 ￥ 49.8 全新
库存29件
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作者周春荔
出版社电子工业出版社
ISBN9787121452833
出版时间2022-09
装帧平装
开本其他
定价49.8元
货号12319081
上书时间2024-12-08
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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 有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
内容摘要
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。
精彩内容
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。
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