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Jingdong book

探秘数学常数:奥妙无穷的黄金分割

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Books Science and Nature Mathematics

Jingdong book

探秘数学常数:奥妙无穷的黄金分割

Name: 探秘数学常数:奥妙无穷的黄金分割
Brand: Jingdong book
SKU: 3137000111
Price: 41.99 USD
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黄金分割是世界上极其美妙的比例，那么，这个神奇的比例是由人类**发现使用还是自然界在亿万年演化过程的选择结果呢？为什么生命世界都对这个数字有莫大的兴趣呢？这本书将为你揭开这神秘的一角。

书中所介绍的知识与我们的生活有重要联系，读者可以看到数学是如何推动科学和技术的发展的；而且本书内容新颖，已涵盖本书印刷前数学研究的新进展和新成果。

书中涉及国内外大量数学家、科学家、艺术家等重要人物，并对相关材料进行了认真梳理和考证，纠正了许多不正确的信息与观点。

本书作者从事数学教学与研究工作数十年，编写出版了20多部科普读物，发表文章500多万字，曾荣获国家科技进步奖二等奖等重要奖项，深受各方赞誉。

Content Description

公元前6世纪，古希腊数学家毕达哥拉斯创立了毕氏学派。在毕氏学派众多辉煌的成就当中，暗含黄金分割比例的正五边形作图法更加璀璨夺目。自此以后2000多年，黄金分割及由此而来的黄金螺线和斐波那契数列引起了无数数学家、科学家、艺术家、建筑师等的巨大兴趣，各种著述层出不穷，并在各个科学和艺术领域以及人们的生活中得到了广泛应用。人们在自然现象中也发现了黄金分割的踪迹。这就是《探秘数学常数：奥妙无穷的黄金分割》所要介绍的内容。
“我喜欢在深夜拨弄心弦，弦上黄金分割不止一点。”相信读了《探秘数学常数：奥妙无穷的黄金分割》，你会成为这样的“φ迷”。

Author Description

陈梅，中学教师。2003年12月获重庆市重点中学中青年教师优质课大赛信息技术学科一等奖。曾担任“站在巨人肩上丛书”（共5册）编委和其中《科学偶然故事》的主编，该丛书获第1届北京市科普作品奖以及第十八届（2002年度）北方十省市（区）科技图书一等奖。担任“七彩学生文库·科学天梯丛书”（共10册）副总主编、编委和其中《科学趣味故事》的主编。参编的《说不尽的π》与《不可思议的e》（“好玩的数学丛书”10册中的两册）获2009年度国家科学技术进步奖二等奖。

陈仁政，中学教师，曾从事中学多科教学。在《数学通报》《物理通报》《化学教学》《知识就是力量》《光明日报》等50多种报刊上，发表各类文章200多篇（次）50多万字，出版著作20多种500多万字。其中“站在巨人肩上丛书”一套5册获第1届北京市科普作品奖以及第十八届（2002年度）北方十省市（区）科技图书一等奖。《说不尽的π》与《不可思议的e》（“好玩的数学丛书”10册中的两册）获2009年度国家科学技术进步奖二等奖。“七彩学生文库·科学天梯丛书”一套10册，获2010年第1届中国科普作家协会科普作品奖提名奖。

Catalogue

第1章毕氏学派——“暗藏黄金”两千年 / 1
1．1临终遗图和洞口的大汉 /1
1．2半岛南端的神秘学派 /2
1．3毕氏学派“暗藏黄金” /6
1．4黄金分割的基本作图、名称和符号 /9
1．5从中末比到黄金分割 /14
1．6不老的传奇 /30
第2章数学中的密码——无处不在的φ /32
2．1φ的18种几何作图方法 /32
2．2φ与黄金螺线 /36
2．3φ与数学形影不离 /48
2．4φ、黄金树与分形 /65
2．5从华尔德、基弗到华罗庚 /66
2．6单因素问题的黄金分割法 /67
2．7单因素问题的分数法 /70
第3章斐波那契数列——兔子奏响的和谐乐章 /72
3．1兔子问题引出F数列 /72
3．2奇妙的F数列 /83
3．3F数列的数学应用 /105
3．4植物与F数列 /144
3．5动物与F数列 /158
3．6电子显微镜下的奇观 /159
3．7F数列用于艺术、文学、体育和建筑 /169
3．8假账单与F数列 /175
3．9F数列娱乐无极限 /176
第4章艺术中的美——艺术家也爱φ /186
4．1比例论引出大明星 /186
4．2绘画和雕塑中的φ /191
4．3建筑中的φ /199
4．4舞台艺术、音乐、文学及书法中的φ /207
4．5φ与摄影 /209
4．6φ在其他场合的应用 /211
第5章生命暗藏的美——生物与φ /212
5．1人体中的φ密码 /212
5．2动物中的φ密码 /215
5．3植物中的φ密码 /218
5．4生物形状的无穷奥秘 /224
第6章从物理学走向宇宙——“没有什么能够阻挡” /227
6．1电学中的φ /227
6．2健康与φ /230
6．3宇宙与自然灾害中的φ /231
第7章自娱自乐会有时——φ的“八卦” /234
7．1五角星中的“黄金” /234
7．2用纸折出正五边形 /238
7．3隐蔽在洛依德谜图中的五角星 /239
7．4五角星与等宽曲线 /239
7．5五角星中摆石子 /243
7．6种树问题中的五角星 /244
7．7一张纸、三根杆和四个键 /245
7．8多米诺骨牌盖棋盘 /246
7．9《红楼梦》和《理想国》中的φ /247
7．10面积的黄金分割 /248
7．11不务正业的“黄金” /249
第8章无穷的探索——φ的悬疑、误区和神话 /251
8．1黄金矩形最美吗 /251
8．2φ的3个误区 /254
8．3φ的两个迷信说法 /255

Introduction

著名数学家哥德尔 18 岁进入维也纳大学时学习的是理论物理专业，他常到位于维也纳第九区斯特鲁德尔霍夫大街 4 号的理论物理研究所 4 楼的大教室聆听奥地利物理学家蒂林的课。有一次，他参加了德国哲学家、物理学家施里克介绍罗素数论著作的研讨会，由此对数理逻辑产生了浓厚的兴趣。数的吸引力如此之大，竟致哥德尔改换门庭。入校两年后，哥德尔放弃了物理学专业，改学数学。 5 年以后的 1931 年， 25 岁的哥德尔发表了震惊数学界的不完备定理。而在今天，用他的姓氏命名的哥德尔奖从 1993 年起每年都在颁发。

提及数学，我们自然无法回避数学常数。最著名的数学常数当属圆周率 π、黄金分割数φ和自然对数的底 e。以色列数学史家马奥尔在《无穷之旅——关于无穷大的文化史》一书中称它们为“ 3 个著名的无理数”。在美国加州谷歌公司总部的 4 座办公大楼中，有 3 座是以这 3 个数学符号命名的。当然，数学中重要的常数远不止于此。
数学常数是古老而又年轻的数论的重要组成部分。虽然截至目前已经取得了许多重大的数论研究成果，但是还有不少谜团让人看朱成碧，不辨五色。正如日本著名数学家弥永昌吉所说，数论的 “大部分仍然笼罩在神奇的面纱之下”。因此，需要我们继续不断探索。“苔花如米小，也学牡丹开。”本丛书作者虽然明知力所不逮，但凭借着对数学常数的浓厚兴趣，自 1982 年开始，断续经过33年的努力，终于编写成了这套系统介绍数学常数的普及读物。这套书包括《说不尽的圆周率》《不可思议的自然对数》《奥妙无穷的黄金分割》《妙趣横生的数学常数》。

虽然目前国内外出版了一些介绍上述三大数学常数的图书，但总体来说不够系统全面，许多有趣的知识没有罗列其中。本套图书希望能在以下方面做出有益探索。
首先，本套图书以 π、φ、 e 等主要的数学常数为主线，但又不限于此，内容涵盖重要数学概念和数学思想的形成、著名公式和定理的证明以及它们在各学科和生活中的应用。单是书中涉及的数学家以及相关的科学家、哲学家等就有 2000 多位，读者可以从书中了解这些著名人物在数学研究中艰难的探索历程（而心怀感恩之情）、所取得的重要成果以及逸闻趣事。
其次，本套图书在化繁为简、深入浅出方面进行了积极的尝试，力求消除“数学是可怕的学科”这样的误解，把“可怕”变为“可爱”，让读者充分感受到数学之真、之美、之乐、之用，感受到数学的魅力。中国数学家张景中在其所著的《数学与哲学》一书开篇就指出：“联系数学的发展历史学习数学哲学，有趣又有效。”在编写过程中，作者也尽力将数学史和科学史内容融入书中，从而梳理出重要数学思想或者数学定理的发展脉络，以及著名数学难题的求解历程。读者感受到的将不再是仅以定理、证明、计算面孔出现的枯燥乏味的脑力训练，而将看到一个有血有肉、充满活力与无限乐趣的新形象。
再次，知识驱动着人类文明的发展，数学作为我们理解和探索科学以及世界的重要工具发挥了重要作用。知识的获取过程是艰辛的，但也充满着乐趣，数学更是如此。本套图书在介绍数学知识之外，更加注重表现数学家的优秀品质以及探索精神，希望读者在享用前人所留下的宝贵精神财富的同时能有一些感触或感悟。
除了作者团队的协作与努力之外，许多专家、学者、朋友及相关人士也对本套图书的编写与出版给与了帮助。在此感谢张景中、李敏、郭书春、宁挺、梁宗巨、张奠宙、査有良、吴振奎、丘和、曾润生、王青建、邹大海、彭定才、潘宁、邓文华、陈文伟、贾小勇、吴至友、罗明、安克·毛雷尔等。由于篇幅所限，还有不少人士的姓名在此未能提及，一并表示感谢。
限于作者的陋见，书中难免存在疏漏与不当之处，请读者批评指正。
爱因斯坦说：“不要担心你在数学上遇到的困难，我敢保证我遇到的困难比你大得多。”让我们以此共勉，并慢慢爱上有趣又好玩的数学吧。

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