高考中的数学文化

本书读者对象主要是高中学生与中学数学教师、试题编制研究人员、师范院校数学专业教师与学生以及数学爱好者等。首先通过数学文化总论对数学文化进行一个系统全面的剖析，然后从数学历史、数学精神、数学应用、数学之美、数学语言、交汇拓展、数学游戏七个方面，遴选近十五年高考数学中涉及数学文化的试题进行分类赏析，系统揭示命制背景、展示解题过程、凸显数学文化价值。把数学文化可能出题的方向尽可能一网打尽，让读者明确数学文化"是什么？”、"怎么考？”、"怎么练？”，为备考数学文化提供清晰的复习方向。同时每个主题后面提供与主题相关的数学文化练习题，作为读者练习巩固使用，以便更有针对性地复习。本书的编写力图实现实用性、针对性和时效性，一方面，密切结合当下学生甚至是教师都对数学文化试题认识相对陌生的客观实际，对高考中曾经出现的数学文化试题进行分类赏析，系统揭示《很新考纲》"考察数学文化”的神秘面纱，同时又想学生之所想，为学生备考提供科学建议。

齐龙新，北京市数学特级教师，山东省教学能手，山东省新课程研修团队专家，山东省基础教育教师培训专家，山东省优质课一等奖、教育部一师一优课一等奖获得者，现为北京市育英学校经济学实验班班主任。作者致力于“新数学自学辅导教学法”的实践与研究，所编自学教材曾获得山东省很好课程资源一等奖，在日常教学实践中也取得了很好显著的教学效果。其微信个人公众号“龙新数学(zxfd66)”曾经获得2016年数学文化杂志社主办的携手北大数学文化节公众号评选全国第二名。
“把数学教得通俗易懂，让学生学得幸福有趣”是作者一以贯之的精致追求，其教学风格独特，教法细腻、技巧纯熟，教学成绩突出，与学生之间亦师亦友，深得学生的喜爱。作者教学之余写出了数十篇教育教学论文，撰写了《初高中数学衔接教材》等多部教研论著。

章 数学文化总论 ··················································································· 1 节 什么是数学文化 ········································································ 1 第二节 数学文化的四个层面 ································································· 3 一、知识系统 ······················································································· 4 二、工具系统 ······················································································· 4 三、价值系统 ······················································································· 5 四、史实系统 ······················································································· 7 第三节 数学文化的人本特性 ································································· 7 一、精神特性 ······················································································· 8 二、物质特性 ······················································································· 8 三、行为特性 ······················································································· 9 四、审美特性 ······················································································· 9 第二章 数学历史 ························································································ 11 节 数学名著 ················································································ 11 一、《九章算术》 ················································································ 12 二、《数书九章》 ················································································ 19 三、《算数书》 ··················································································· 24 第二节 数学故事 ················································································ 27 一、毕达哥拉斯的故事 ········································································· 27 二、高斯的故事 ·················································································· 36 三、哥德巴赫的故事 ············································································ 41 第三节 数学名题 ················································································ 44 一、米勒问题 ····················································································· 45 二、斐波那契数列 ··············································································· 57 三、阿基米德穷竭法 ············································································ 66 四、柯西不等式 ·················································································· 73 五、角谷猜想 ····················································································· 80 六、阿波罗尼奥斯圆 ············································································ 85 七、回文数 ························································································ 93 八、勾股数 ························································································ 98 九、平均数 ······················································································· 101 十、皮克定理 ···················································································· 108 十一、数字黑洞 ················································································· 114 十二、伯努利不等式 ··········································································· 119 十三、正整数方幂和 ··········································································· 124 十四、切比雪夫多项式 ········································································ 130 十五、马尔科夫定理 ··········································································· 135 十六、四色问题 ················································································· 143 十七、莱布尼茨三角形 ········································································ 146 十八、黄金分割比 ·············································································· 151 第三章 数学精神 ······················································································· 155 节 理性求真 ··············································································· 155 第二节 创新意识 ··············································································· 167 第四章 数学应用 ······················································································· 177 节 营销决策类 ············································································ 178 第二节 金融经济类 ············································································ 183 第三节 环境保护类 ············································································ 188 第四节 建设工程类 ············································································ 195 第五节 交通运输类 ············································································ 204 第六节 概率统计类 ············································································ 209 第七节 日常民生类 ············································································ 218 第五章 数学之美 ······················································································· 227 节 和谐美 ··················································································· 227 一、结构形式的和谐统一 ····································································· 228 二、项、项数、次数的和谐统一 ···························································· 235 三、转换的和谐统一 ··········································································· 239 第二节 简洁美 ··················································································· 242 第三节 对称美 ··················································································· 248 第四节 奇异美 ··················································································· 253 一、解法多样的奇异美 ········································································ 254 二、解法之巧的奇异美 ········································································ 259 第六章 数学语言 ······················································································· 264 第七章 交汇拓展 ······················································································· 272 第八章 数学游戏 ······················································································· 276 附录一 本书习题参考答案 ········································································· 285 附录二 高考数学文化最新动态 ································································· 325 参考文献 ···································································································· 344