描述
开 本: 16开纸 张: 胶版纸包 装: 平装-胶订是否套装: 否国际标准书号ISBN: 9787121316371丛书名: 数学文化系列丛书
★为什么要学习数学文化？其实这个问题也等同于为什么要学习数学。数学本身就是一种文化，所以这本书旨在帮助学生形成良好的数学思维能力，掌握解决问题的方法，培养理性精神。
★现在的高考试题越来越注重考生解决问题的能力，倘若只会刷题而不能理解题中真意将会寸步难行。本书以文化为内核，将理论、方法、历史、文化融为一体，知识性、趣味性和实操性完美结合。
★数学家顾沛高度赞赏的数学文化典范之作，中国科学院院士陈佳洱、王大中联袂诚意推荐，适合高中生及教学工作者使用。
*考试中心以正式文件明确提出在高考数学考题中要体现数学文化，这是一个明显的信号：要求学生加强对数学文化知识的学习，自觉地、有针对性地重视对数学文化修养的提升。
本书创新性地从“以数化人”与“人数学化”两个角度来谈数学文化，对数学文化在数学历史、数学精神、数学应用、数学之美、数学语言、交汇拓展、数学游戏等各个主题上都作出了全面透彻的剖析和论述。除此之外，作者还结合历年高考数学试题进行具体的案例分析，以此让高考生能够精准消化吸收高考中的各种数学文化考点。
对高中生而言，这是一部让他们明确数学文化“是什么”“怎么考”“怎么练”，为高考数学文化题型提供清晰解题思路的红宝书；对数学教学工作者或研究者而言，这是一部系统揭示命制背景、展示解题过程、凸显数学文化价值的宝贵内参书；对于广大的数学文化爱好者而言，这又是一部让人崇尚真理，净化心灵，提升文化修养和文化品格的数学美书。
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 ·······················
2016
年10 月8 日，*考试中心下发《关于2017 年普通高考考试大纲修订内容的通知》（教试中心函〔2016〕179 号），增加了数学文化的要求。这一文件的公布，引发了社会对数学文化的极大关注，成为教育界的热门话题。
事实上，当人们不满足于对数学本身的研究，开始从外部审视数学的价值时，对数学文化的研究就开始了。人们开始思考“数学是什么”与“数学的价值是什么”，并逐渐认识到数学已经成为人类文化的重要组成部分，在过去已经对人类文明做出了巨大的贡献，在未来也必将做出更大的贡献。
把数学作为文化来进行研究，国外要比我们早很多，比较有代表性的是美国的数学家怀尔德与数学史专家莫里斯·克莱因。怀尔德认为数学是一个由内在力量与外在力量共同作用，而处于不断发展和变化之中的文化系统。数学文化是由文化传统和数学本身所组成。这些观点在他的两部著作《数学概念的演化》和《作为一种文化系统的数学》中得以充分体现。莫里斯·克莱因在他的著作《西方文化中的数学》《数学：一种文化探索》《数学与知识的探求》中则系统论述了数学对西方文化、理性精神、现代人类思想发展所产生的影响。他侧重于数学与各种文化以及社会因素之间相互作用的分析。我国开展数学文化研究是近二三十年的事情，时间虽短，但是相关研究也取得了极大进展。徐利治探讨数学一般意义上存在的某些相同或不同的方法，开创了“数学方法论”的研究与教学；郑毓信教授在他的《数学文化学》中基于数学哲学观点构建数学文化学的理论体系，尝试从理论层面论述数学作为文化的内涵；齐民友在《数学与文化》一书中则论述了中西数学文化的差异。
我国教育主管部门对数学文化也很重视。早在2003 年，*颁布的《普通高中数学课程标准（实验）》中就突出强调了数学的文化价值——数学是人类文化的重要组成部分，对数学文化给予了特别重视，要求数学文化贯穿整个高中数学课程并融入教学中。这次*考试中心又再次以发布正式文件的方式对数学文化重点提及，明确提出要在高考试题中考查数学文化，足以看出国家对数学文化的重视。
以往提及数学文化，大多停留在理论的层面，而且很多研究仅仅把史实、案例、故事等稍作整理，将数学史等同于数学文化。这种做法不过是给数学文化穿了件“数学史”外衣而已。类似的研究总给人以不接地气之嫌，没有引起人们的触动。但这次之所以引发对数学文化思考与研究的热潮，主要原因是考试主管部门从考试命题的角度提出了要求，次正式地明确要求把数学文化渗入数学试题，所以未来高考数学命题肯定会遵照执行。虽然我们提了很久的数学文化，但如何在数学试题中体现出来，对很多人来说还是比较陌生的。数学文化本来是个笼统的概念，传统意义上“文化”在文科中出现得较为普遍，在文科类的命题中是很容易做到的。而数学是逻辑的科学、思维的科学，如何把“文化”渗透其中，是一个摆在广大数学教育工作者面前的新课题。正是在这样的背景下，我根据多年积累的丰富资料和大量的研究工作，捉笔成书，对相关问题作出了系统的回答。
《高考中的数学文化》一书共分八章。章为数学文化总论，主要阐述了数学文化的含义、内容和基本特性等问题；后面七章分别为数学历史、数学精神、数学应用、数学之美、数学语言、交汇拓展、数学游戏，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。全书尽可能把数学文化出题的方向一网打尽，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，方便读者练习巩
固使用，从而更有针对性地复习。本书的编写具有实用性、针对性和时效性三个鲜明特点，密切结合当下学生、教师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，系统阐述“考纲”考查数学文化的内涵，同时为学生备考提供科学性的建议。
我国对数学文化的系统研究时间不长，尤其是数学文化与试题的结合研究更是不成熟。此书尽管对数学文化的理论探讨与应用研究取得了较大突破，然而也不免出现不完善或者纰漏之处。但我相信，此书的问世将会受到广大同行的重视和学生的欢迎。在此，我也恳请读者批评雅正。
数学是人类文化的重要组成部分，数学是人类文明进步的产物，也是推动社会发展的动力。通过对本书数学文化的学习，学生可以初步了解数学的思想精神，了解数学科学与人类社会发展之间的相互作用，体会数学的科学价值、应用价值、人文价值和审美价值，开阔视野，感受数学家治学的严谨，寻求数学发展的历史轨迹，探索数学发展的不同阶段，激发对数学的兴趣和对数学创新的认识，从而提高自身的文化素养、思想素养和创新意识。
——数学家顾沛
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