内容简介
本书主要介绍了勾股定理的 365 种证明方法, 并按证法的类型进行归纳、整理和总结, 让 读者有一个全面而系统的了解. 书中大多数证法用到的知识不超过初中几何的教学范围, 许多证法思路巧妙, 别具一格, 对提高读者的几何素养大有裨益. 本书可以作为广大中学师生和数学爱好者的参考读物.
目录
第1 章分块法......................................................................................1
1.1 分块对应法.............................................................................2
1.2 镶嵌法....................................................................................8
1.3 十字分块法............................................................................12
第2 章割补法.....................................................................................17
第3 章搭桥法.....................................................................................23
第4 章“化积为方”法.........................................................................38
第5 章等积变换法..............................................................................45
第6 章拼摆法.....................................................................................57
第7 章增积法.....................................................................................78
第8 章消去法.....................................................................................95
8.1 倍积法...................................................................................95
8.2 面积比例法..........................................................................102
第9 章同积法...................................................................................111
第10 章射影法.................................................................................131
10.1 作斜边垂线的证法..............................................................131
10.2 作直角边垂线的证法...........................................................139
第11 章长度法.................................................................................142
第12 章方程法.................................................................................152
第13 章平方差法..............................................................................157
第14 章辅助圆法..............................................................................163
第15 章相似转化法..........................................................................172
第16 章间接证法..............................................................................177
16.1 反证法...............................................................................177
16.2 同一法...............................................................................178
第17 章解析法.................................................................................183
17.1 坐标法...............................................................................183
17.2 参数法...............................................................................191
17.3 三角函数法........................................................................193
第18 章特例法.................................................................................198
第19 章泛化法.................................................................................208
附录A 证法出处汇总.........................................................................232
附录B 勾股定理的365 种证明有用吗?..............................................243
参考文献..............................................................................................246
后记.....................................................................................................247
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