具体描述
The author's purpose is to share the thrills and excitement of ingenious solutions to intriguing elementary problems that he has had the good fortune to have conceived in the pursuit of his passion over many years. His satisfaction lies in the beauty of these gems, not in the incidental fact that they happen to be his own work. A wonderful solution is a glorious thing, whoever might have thought of it, and the author has worked diligently to make easy reading of the joy and delights of his often hard-won success.
As Director, responsible for composing the problems for the New Mexico Mathematics Contest before his retirement, the author consulted the wonderful books by Professor Ross Honsberger whenever he needed an inspiration. As a result, the New Mexico Mathematics Contest rose to national prominence and the author received the “Citation for Public Service” from the American Mathematical Society in 1998. In this volume he collected his treatments of over a hundred problems from the treasure trove of Professor Honsberger.
Perhaps it is best to quote Professor Honsberger, “This is a book for everyone who delights in the richness, beauty, and excitement of the wonderful ideas that abide in the realm of elementary mathematics. I feel it is only fair to caution you that this book can lead to a deeper appreciation and love of mathematics.”
作者简介
Liong-shin Hahn
Liong-shin Hahn was born into a family of physicians in Tainan, Taiwan. He calls himself the black sheep of the family, because, like his father, Shyr-Chyuan Hahn, M.D., Ph.D., all five of his brothers became physicians. After graduating from Tainan First Senior Middle School and the National Taiwan University, he attended Stanford University and obtained his Ph.D. there under Professor Karel deLeeuw. He spent most of his career at the University of New Mexico, and while away from that institution, he held visiting positions at the University of Washington (Seattle), the National Taiwan University, the University of Tokyo, Sophia University (Tokyo) and the International Christian University (Tokyo). As director of the mathematics contest sponsored by the University of New Mexico, he consulted frequently the superb books by Professor Ross Honsberger that seeded the birth of this book. He authored Complex Numbers and Geometry (Mathematicial Association of Americia, 1994), New Mexico Mathematics Contest Problem Book (University of New Mexico Press, 2005), and co-authored with Bernard Epstein Classical Complex Analysis (Jones and Bartlett, 1996). He was awarded the Citation for Public Service from the American Mathematical Society in 1998. His marriage to Hwei-Shien Lee (yet another M.D.) yielded three sons and seven grandchildren.
著者信息
图书目录
Contents
Introduction vii
Preface viii
1 Mathematical Delights 1
1.1 Triangles in Orthogonal Position 1
1.2 Pan Balance 6
1.3 Schoch 3 7
1.4 A Nice Problem in Probability 10
1.5 Three Proofs of the Heron Formula 13
1.6 Incenter 18
1.7 On Median, Altitude and Angle Bisector 19
1.8 A Geometry Problem from Quantum 23
1.9 Monochromatic Triangle 25
1.10 Sum of the Greatest Odd Divisors 26
1.11 Prime Numbers of the Form m2k + mknk + n2k 27
2 In P olya's Footsteps 29
2.1 Curious Squares 29
2.2 A Problem from 15th Russian Olympiad 32
2.3 Maximum Without Calculus 34
2.4 Cocyclic Points 36
2.5 Reconstruction of the Original Triangle 37
2.6 The Sums of the Powers 38
2.7 A Problem from Crux Mathematicorum 46
2.8 A Puzzle 47
2.9 Pedal Triangle with Preasigned Shape 47
2.10 An Intriguing Geometry Problem 49
3 Mathematical Chestnuts from Around the World 52
3.1 Three Similar Triangles Sharing a Vertex 52
3.2 The Simson Line in Disguise 55
3.3 Circle through Points 56
3.4 Zigzag 57
3.5 Cevians 60
3.6 Integers of a Particular Type Divisible by 2n 61
3.7 Quadrangles with Perpendicular Diagonals 61
4 Mathematical Diamonds 64
4.1 Orthic Triangle 64
4.2 Quartering a Quadrangle 66
4.3 A Well-Known Figure 67
4.4 Rangers with Walkie-Talkie 71
4.5 A Piston Rod 73
4.6 The Schwab-Schoenberg Mean 75
4.7 Construction of an Isosceles Triangle 79
4.8 The Conjugate Orthocenter 82
4.9 A Remarkable Pair 85
4.10 Calculus? 89
4.11 A Problem from the 1980 Tournament of Towns 91
5 From Erdos to Kiev 96
5.1 The Sum of Consecutive Positive Integers 96
5.2 A Problem in Graph Theory 98
5.3 A Triangle with its Euler Line Parallel to a Side 99
5.4 A “Pythagorean” Triple 102
5.5 A Geometry Problem from the K?ursch?ak Competition 104
5.6 A Lovely Geometric Construction 109
5.7 A Problem from the 1987 Austrian Olympiad 112
5.8 Another Problem from the 1987 Austrian Olympiad 116
5.9 An Unexpected Property of Triangles 119
5.10 Products of Consecutive Integers 125
5.11 A Problem from the Second Balkan Olympiad, 1985 129
A Exercises 136
B Solutions 166
C Useful Theorems 288
C.1 Triangles 288
C.1.1 Complex Plane 288
C.1.2 Corollaries 290
C.1.3 Equilateral Triangles 291
C.1.4 Theorems of Ceva and Menelaus 291
C.2 Circles 294
C.2.1 Subtended Angles 294
C.2.2 The Power Theorem 297
图书序言
Preface
Before my retirement, I was responsible for composing the problems for the New Mexico Mathematics Contest1. Whenever I needed an inspiration then, I always turned to the wonderful books by Professor Ross Honsberger. I knew his books were a treasure trove of interesting problems with brilliant solutions. So it was only natural that when I retired and wanted to prevent dementia, I chose problems from his books for my “Problem-of-the-Day” activity. I would not peek at the solution unless I had solved the problem myself, or could not come up with a fresh approach to tackle the problem for at least 72 hours. The problem-of-the-day activity gave me a daily drama. Some days, I was delighted to have found nice solutions, but some other days I was disappointed that my “brilliant” solutions turned out to be essentially the same as those presented in his books, or worse, not so brilliant compared to the published ones.
Time and again, Professor Honsberger encouraged me to publish my solutions. This book is the consequence. I can only claim I found these solutions myself. But as it is irrelevant for my problem-of-the-day activity, no effort is made to check whether they are new. Naturally, my solutions that have already appeared in Professor Honsberger's books are excluded. On the other hand, some solutions that are not so elegant are included, in the hope that they still have some merits. By the way, my original plan was to include also Episodes in Nineteenth and Twentieth Century Euclidean Geometry, which is another very rich source for exploration. However, my manuscript is already over 300 pages, and the inclusion would make this one too lopsided toward geometry. Furthermore, after five years on this book project, I am eager to move on to the next phase of my life.
Each chapter corresponds to Professor Honsberger's book with the same title. However, the order of the chapters is random, and so they can be read in any order. Yet, in Exercises (Appendix A) and Solutions (Appendix B), I preserve the order in Professor Honsberger's books for easy reference. The source of each problem is identified by a single or a pair of number(s) in brackets. For example, because Chapter 2 corresponds to In P?olya's Footsteps, so a problem taken from page 67 of In P?olya's Footsteps is indicated by [67] in Chapter 2, while this same problem is referred to in other chapters by [2:67]. None of the problems in Exercises (Appendix A)1See my book, New Mexico Mathematics Contest Problem Book (University of New Mexico Press, 2005).popped out of thin air. If they have appeared in Professor Honsberger's books, then alternate solutions can be found in Solutions (Appendix B). Others are byproducts of my solutions. Therefore, all have their origins, directly or indirectly, in Professor Honsberger's works. Appendix C is designed to provide sufficient background for the readers. It contains my favorite “tools of the trade”.
I am an unabashed admirer of the late Professor George P?olya, mainly for the elegance of his mathematics, but also for his teaching and problem-solving methods, not to mention his devotion to mathematics education.
I keep on telling students whenever I have a chance: “If you find a book by Professor P?olya, buy it and read it. You will be happy you did.” His books are invaluable for anyone in mathematics, both in teaching and in research. I only wish I had a chance to hear his comments on my solutions. I am sure many readers can detect his influence on me.
Although Professor Honsberger's books are not a necessary background; i.e., this book can be read independently, I am sure, by parallel reading, the reader will be all the more entertained. And I certainly hope that readers who enjoy his books will also enjoy mine. At the minimum, I hope I have some success in conveying the joy of problem solving.
It is a pleasure to express my heartfelt appreciation to Professor Honsberger for his friendship over the decades, and his encouragement throughout this book project. I can never thank him enough for his very meticulous reading of the manuscript and generous help in improvement of the presentation, not to mention his endorsement in the Introduction.
L.-s. H.
February 2008
Postscript. It is a pleasure to express my deep appreciation to Dr. Luke Cheng-chung Yu (neonatology and pediatric cardiology, board certified) and my son, Shin-Yi, for their help in solving the computer problems for me. Without their help, I don’t know how long the publication of this book would have been delayed. Even though the manuscript was completed in February 2008, it was submitted to the National Taiwan University Press three years later. Knowing the book will be published within one year was a happy surprise for the author. Now the fortunate result is before you.
中文说明
本书(中译名：重访亨斯贝尔格--磨亮数学宝石)是美国 New Mexico 大学退休教授 Liong-Shin Hahn（韩良信）从着名数学家 Ross A Hongsberger 所着的五本书中选出好题目，加以探索、分析、解题、延伸之后，写下的一本「读数」札记。
Hongsberger 的这五本书分别是(1) Mathematical Delights(2004出版) (2) In Polya's Footsteps(1997出版) (3) Mathematical Chestnuts from around the world(2001出版) (4) Mathematical Diamonds(2003出版) (5) From Erd?s to Kiev(1996出版)。
韩教授将上述这五本书的书名作为本书的章名，每一章的题目都是从 Hongsberger 对应的书中挑出来的，并且提供了比原书更好，更精致，且更具启发性的解法。作者特别强调「重访」这本书完全可以独立阅读，当然也可以与 Hongsberger 的原书平行阅读。
除了上述五章本文之外，「重访」一书另有A、B、C三个附录。附录A收集了115个挑战题，粗分为52题几何题，20题代数题，18题数论题，20题组合题和5题微积分题，解题所需的工具是高中数学。
附录B是对附录A的详解。附录C是整本「重访」一书解题所需的定理，作者将这些定理作了很好的证明和延伸，这些定理包含了中学教育最核心的议题：
c.1 三角形相关定理
c.2 圆形相关定理
c.3 三角学相关定理
c.4 圆锥曲线相关定理
c.5 Jensen不等式的各种面貌
本书不单是一本解题手册，而是借解题来呈现作者认为最重要的数学，适合对数学有兴趣的高中生、大学生以及中学的数学教师研读。
Introduction
What is it about math problems that makes them so addictive?
When I get going on a problem, I’d rather stay at it than eat!
Liong-shin Hahn and I are kindred spirits who have lived like this for the last fifty years. As you might expect, Liong-shin has become very adept at solving problems, and in this volume he has collected his treatments of some hundred problems that caught his eye in my books. If you would like a sample of his ingenuity, take a look at Exercise 49 (pages 149 and 215) or his solution to Exercise 8 (pages 138 and 177); and wait till you see what Problem 2.1 (page 29) conjured up in his mind!
While this volume might be used in the training of young scholars to write mathematics contests, it is more than that. This is a book for everyone who delights in the richness, beauty, and excitement of the wonderful ideas that abide in the realms of elementary mathematics. I feel it is only fair to caution you that this book can lead to a deeper appreciation and love of mathematics.
Without further ado, then, let us turn over the stage to this remarkable man—Liong-shin Hahn.
By Ross Honsberger.
图书试读
用户评价
当我拿到《Honsberger Revisited：Mathematical Gems Polished》这本书时，我并没有抱有太高的期望，毕竟数学普及类的书籍琳琅满目，能真正触动人心的并不多。然而，这本书却给了我一个巨大的惊喜。它以一种极为巧妙的方式，将那些深奥的数学概念，转化为一个个引人入胜的故事和问题。我并非数学科班出身，但这本书的讲解方式，让我能够轻松地理解那些原本可能令人望而却步的数学知识。作者仿佛是一位经验丰富的向导，他并没有强迫你一次性接受所有信息，而是耐心地引导你，让你在自己的节奏下，慢慢地领略数学的魅力。我最欣赏的是书中对于“反常识”的数学现象的介绍。很多时候，我们直觉上的判断在数学的世界里是行不通的，而这本书就善于揭示这些“反常识”之处，让你不禁感叹数学的神奇。我记得书中有一个关于概率的问题，它挑战了我一直以来的认知，让我对随机事件有了全新的理解。这种“颠覆认知”的体验，是学习过程中最宝贵的财富之一。这本书的叙述语言十分优雅，既有学术的严谨，又不失文学的韵味。作者在讲解数学问题的过程中，会穿插一些历史故事和名人轶事，让整个学习过程变得更加生动有趣。我甚至在阅读过程中，会不自觉地被作者的文笔所吸引，仿佛在品读一本优秀的散文集。这本书的装帧设计也十分精美，纸张的触感和墨水的味道，都传递出一种高品质的阅读体验。我常常会把这本书放在床头，睡前翻几页，让数学的智慧陪伴我入眠。总而言之，这是一本能够让你在轻松愉快的氛围中，提升数学素养的书。它不仅能够拓展你的知识面，更重要的是，它能够激发你对数学的兴趣，让你看到数学的无限可能。
评分《Honsberger Revisited：Mathematical Gems Polished》这本书，在我看来，是一次对数学本质的深刻挖掘与优雅呈现。它不像许多泛泛而谈的科普读物，而是精选了一系列具有代表性的“数学珍宝”，并对其进行了细致入微的打磨。我特别喜欢书中对每一个“珍宝”的介绍方式，它不是简单地罗列公式和定理，而是从一个具体的问题出发，引导读者逐步走向深刻的数学洞察。这种“由果溯因”的讲解模式，让我更能理解数学知识的由来和应用。我印象最深刻的是书中一个关于图论的例子。作者通过一个简单的城市交通网络问题，巧妙地引入了图论的概念，并展示了如何用数学工具来解决实际问题。这个例子让我对图论产生了浓厚的兴趣，也让我认识到数学并非遥不可及，而是与我们的生活息息相关。这本书的语言风格非常独特，既有数学的严谨性，又不乏幽默感。作者在解释复杂概念时，经常会运用形象的比喻和生动的类比，让我能够更容易地理解和记忆。我甚至在阅读过程中，会时不时地会心一笑，被作者的幽默所感染。这种寓教于乐的学习方式，是我非常看重的。此外，书中那些精美的插图和数学模型，更是为整个阅读体验增色不少。它们不仅仅是文字的辅助，更是将抽象的数学概念具象化，让我能够更直观地感受到数学的美。我经常在阅读时，一边对照图表，一边跟着作者的思路推导，这种沉浸式的学习体验，让我受益匪浅。总而言之，这是一本能够让你在不知不觉中，爱上数学的书。它不仅能够拓展你的数学视野，更重要的是，它能够培养你独立思考和解决问题的能力。
评分我必须说，在读完《Honsberger Revisited：Mathematical Gems Polished》之后，我的数学观被彻底颠覆了。我一直以为数学是那些严谨、刻板、只存在于书本上的抽象概念，但这本书彻底打破了我的刻板印象。它以一种极其生动、富有启发性的方式，将那些隐藏在日常生活和社会中的数学规律和美感揭示出来。我尤其喜欢书中对于“巧思”的强调。很多时候，解决一个数学难题的关键，不在于你掌握了多少复杂的公式，而在于你是否能找到一个巧妙的角度，或者一个简单的逻辑。这本书就像是一个宝库，里面陈列着无数这样的“巧思”，它们如同精美的艺术品，让人赞叹不已。例如，书中有一个关于排列组合的问题，看似复杂，但作者通过一个简单的模型，就将其变得清晰明了。我当时就有一种豁然开朗的感觉，后悔自己之前为什么没有想到这一点。这种“顿悟”的时刻，是学习过程中最令人兴奋的体验。这本书的结构设计也非常合理，每一个“数学珍宝”都被独立地呈现出来，但又相互关联，形成了一个有机整体。你可以按照自己的节奏来阅读，或者跳读你感兴趣的部分。我个人倾向于逐章阅读，这样更能感受到作者循序渐进的引导，以及数学概念之间的内在联系。书中那些精美的插图和图表，更是锦上添花，它们不仅仅是为了说明问题，更是将抽象的数学概念可视化，让你更容易理解和记忆。我记得有一个关于不动点定理的讲解，书中用了一个生动的例子，并配以精美的图示，让我一下子就理解了那个曾经困扰我的定理。这不仅仅是一本学习数学的书，更是一本激发思考、培养创意的书。它让我看到了数学在各个领域的应用，也让我对数学的未来充满了无限的憧憬。
评分自从我开始阅读《Honsberger Revisited：Mathematical Gems Polished》这本书以来，我仿佛进入了一个全新的数学世界。它不再是那些令人生畏的定理和公式，而是充满了惊喜和发现的奇妙旅程。我最欣赏的是书中对于“数学的优雅”的展现。作者并非简单地罗列知识点，而是通过精心设计的讲解，让你体会到数学逻辑的精巧和数学结论的美妙。我记得书中有一个关于斐波那契数列的讲解，作者从一个简单的兔子繁殖问题出发，逐步引出了斐波那契数列的各种神奇性质。这种“层层深入”的讲解方式，让我能够真正地理解和欣赏这个数列的美。此外，书中那些“意想不到”的数学联系，更是让我惊喜连连。作者善于将看似无关的数学概念联系起来，让你看到数学的统一性和深刻性。我甚至在阅读过程中，会时不时地停下来，思考作者提出的问题，并尝试自己去寻找答案。这种主动的学习方式，让我更加深入地理解了书中内容。这本书的语言风格也十分简洁有力，作者用最精炼的语言，表达了最深刻的数学思想。我常常在阅读时，会被作者的文字所吸引，仿佛在品读一首优美的诗歌。这本书的装帧设计也极具艺术感，书的整体风格沉稳而大气，透露出一种知识的力量。总而言之，这是一本能够让你在享受阅读乐趣的同时，对数学产生浓厚兴趣的书。它不仅能够拓展你的知识广度，更重要的是，它能够培养你发现数学之美的能力。
评分《Honsberger Revisited：Mathematical Gems Polished》这本书，对于我来说，不仅仅是一本关于数学的书，更是一次与智者对话的经历。它以一种独特的方式，将那些曾经令我感到遥不可及的数学概念，变得鲜活而生动。我特别喜欢书中那种“循循善诱”的讲解风格。作者并没有直接告诉你答案，而是引导你一步步地去思考，去探索，去发现。这种“自己动手”的解决问题的过程，让我更加深刻地理解了数学的本质。我印象最深刻的是书中一个关于“鸽笼原理”的讲解。作者通过一个生动的例子，让我一下子就明白了“鸽笼原理”的精妙之处。那种“豁然开朗”的感觉，是任何一种死记硬背都无法给予的。此外，书中那些“数学的趣味性”的呈现，更是让我惊喜连连。作者在讲解数学问题的过程中，会穿插一些有趣的谜题和悖论，让整个学习过程变得更加轻松愉快。我甚至在阅读过程中，会时不时地和家人朋友讨论书中的内容，分享我的学习心得。这种交流和分享，让我更加巩固了对知识的理解。这本书的排版设计也十分考究，文字清晰，图表精美，给人一种赏心悦目的感觉。我甚至会反复翻阅书中的一些插图，试图从中发现更多的数学信息。总而言之，这是一本能够让你在享受阅读乐趣的同时，大幅提升数学思维能力的书。它不仅能够拓展你的知识维度，更重要的是，它能够培养你对数学的热情和好奇心。
评分我必须承认，《Honsberger Revisited：Mathematical Gems Polished》这本书，在我沉寂已久的数学热情中，点燃了一簇新的火焰。我曾一度认为，数学只是枯燥的公式和抽象的符号，但这本书彻底改变了我的看法。它用一种极其富有感染力的方式，将数学的“美”和“趣味”展现在我面前。我尤其喜欢书中对“数学思维”的强调。很多时候，一个看似复杂的问题，可能只需要一个简单的数学思想，就能迎刃而解。这本书就像是一本“思维宝典”，里面蕴含着无数解决问题的“绝招”。我记得书中有一个关于整数分拆的问题，我之前尝试了各种方法都无从下手。当读到书中作者提供的“生成函数”的思路时，我才豁然开朗，那种“原来如此”的惊喜，至今难忘。这种“点石成金”的智慧，正是这本书的魅力所在。作者的叙述风格也非常流畅，他善于将复杂的数学概念，用通俗易懂的语言进行解释，同时又不失其深刻内涵。我常常在阅读过程中，会不自觉地跟着作者的思路一起思考，仿佛在进行一场有趣的头脑风暴。这本书的排版设计也十分出色，文字清晰，图表精美，给人一种高雅而舒适的阅读感受。我甚至会反复翻阅书中的一些图示，试图从中发现更多的数学细节。总而言之，这是一本能够让你在享受阅读乐趣的同时，大幅提升数学能力的著作。它不仅能够拓展你的知识边界，更重要的是，它能够让你领略到数学作为一门艺术的魅力。
评分对于我而言，《Honsberger Revisited：Mathematical Gems Polished》是一次久违的智力冒险，更是一场感官与思维的双重盛宴。这本书并非市面上常见的“速成”指南，而是一本需要读者静下心来，用心去品味的著作。它就像一位技艺精湛的珠宝匠，将一颗颗未经打磨的数学原石，精心雕琢成闪耀夺目的宝石，然后一件件地展示在读者面前。我喜欢书中那种“抽丝剥茧”的讲解方式。作者不会急于给出结论，而是引导你一步步地去探索，去发现。每一个数学问题都像是一个等待被解开的谜团，而作者的叙述，就像是为你点亮了前进道路上的火把。我常常在阅读过程中，一边跟着作者的思路思考，一边在脑海中勾勒出各种可能的解决方案。有时候，我会尝试自己去推导，去验证，即使遇到困难，也不会感到沮丧，反而会更加激发我的斗志。因为我知道，最终的答案，一定隐藏在作者的笔下，等待我去发掘。书中那些“数学珍宝”的选取，更是体现了作者的独到眼光。它们不仅仅是那些枯燥的定理和公式，而是那些能够激发你思考、让你眼前一亮的数学“妙趣”。我记得有一个关于数论的问题，我之前从未接触过，但通过作者的讲解，我却能体会到其中蕴含的深刻逻辑和简洁之美。这种“美的体验”，是任何一种枯燥的解题练习都无法给予的。这本书的排版和设计也堪称一流。每一个数学公式都清晰易懂，每一个图表都精心绘制，给人一种赏心悦目的感觉。我甚至会反复翻阅书中的图表，试图从中发现更多的细节和信息。总而言之，这是一本值得反复阅读、反复思考的书。它不仅能够提升你的数学知识，更重要的是，它能够培养你对数学的热爱，以及独立思考和解决问题的能力。
评分这本书的封面设计就透着一股沉静而又充满智慧的吸引力，深沉的蓝色搭配金色的书名，仿佛是在预示着里面蕴含着的是经过岁月打磨、光彩夺目的数学珍宝。我是在一个偶然的机会接触到这本《Honsberger Revisited：Mathematical Gems Polished》的，当时对这个名字就产生了浓厚的兴趣，“Revisited”暗示着对经典的回顾和升华，“Mathematical Gems”则明确了其内容的核心——那些数学领域中闪耀的、令人惊叹的宝藏。“Polished”更是点睛之笔，说明这些宝石并非未经雕琢，而是经过精心打磨，以最清晰、最 elegant 的方式呈现给读者。我的数学背景不算特别深厚，更多的是一种对未知世界的好奇和探索欲，所以当我翻开这本书时，并没有抱着要啃下高难度定理的决心，更多的是一种学习和欣赏的心态。我喜欢它那种循序渐进的讲解方式，虽然涉及的数学概念可能对于初学者来说有些挑战，但作者 Honsberger 先生（或者说是这本书的作者团队，如果不是直接由 Honsberger 本人编写的话，但无论如何，其精神和风格都被很好地继承和发扬了）的叙述方式非常生动有趣，仿佛一位经验丰富的向导，耐心地引领着我穿越数学的丛林。他善于用直观的例子和巧妙的比喻来解释抽象的概念，这一点对我来说至关重要。我经常发现自己在阅读过程中会不自觉地停下来，反复咀嚼作者的文字，甚至会拿纸笔演算一下，试图亲身体验那种“aha moment”。这本书不仅仅是知识的堆砌，更是一种思维方式的启迪。它教会我如何去观察，如何去分析，如何去寻找问题背后更深层次的结构。即使是那些我之前从未接触过的数学分支，通过作者的讲解，也变得不再那么令人望而却步。我尤其喜欢书中那些“未解之谜”或者“待探索的领域”的介绍，它们像是在我面前打开了一扇扇通往更广阔数学世界的大门，激发了我进一步学习的动力。这本书的排版也很精美，插图和图表的运用恰到好处，极大地提升了阅读体验。总而言之，这是一本我非常愿意推荐给任何对数学怀有好奇心的人的书，无论你是数学专业的学生，还是仅仅是对此领域感到兴趣的业余爱好者，都能从中受益匪浅。它不仅仅是一本教科书，更像是一本充满智慧和启发的读物。
评分当我捧起《Honsberger Revisited：Mathematical Gems Polished》这本书时，我首先被其沉静而又充满智慧的书名所吸引。它仿佛承诺着一场关于数学的探索之旅，而这本书也确实不负众望。我并非科班出身的数学专业人士，更多的是对世界运行规律的好奇，而这本书恰好满足了我这种探索欲。它没有过于艰涩的术语，也没有高不可攀的理论，而是以一种“润物细无声”的方式，将一个个精妙绝伦的数学“宝石”呈现在我眼前。我尤其欣赏书中对于“问题的解构”的处理方式。作者往往会先提出一个看似简单，却又蕴含深刻道理的问题，然后一步步地引导读者去分析，去思考，去寻找解决问题的钥匙。这种“引导式”的学习过程，比直接给予答案更能激发人的内在动力。我记得书中有一个关于排列组合的问题，我之前总是凭感觉去猜测，结果屡屡出错。当读到书中作者用“分类讨论”和“排除法”来解决这个问题时，我才恍然大悟，原来解决问题的关键在于清晰的逻辑思路。这种“拨云见日”的体验，让我受益匪浅。此外，书中那些跨越不同数学领域的“连接”，更是让我看到了数学的宏大与统一。作者仿佛一位技艺高超的织匠，将零散的数学知识点，编织成一幅幅精美的画卷。我甚至在阅读过程中，会不自觉地将书中的数学思想应用到我的日常思考中。这本书的排版设计也极为用心，文字的疏密有致，图表的精巧绘制，都让阅读成为一种享受。总而言之，这是一本能够让你在轻松愉快的阅读体验中，深刻领略数学魅力，并培养独立思考和解决问题能力的书。
评分作为一名多年的数学爱好者，我曾涉猎过不少数学普及读物，但《Honsberger Revisited：Mathematical Gems Polished》给我的感受绝对是独一无二的。这本书并非那种填鸭式的知识灌输，而是以一种非常“亲切”的方式，将一个个精巧绝伦的数学问题呈现在读者面前。我可以感觉到，作者在字里行间流露出的那种对数学的热爱和对美的追求，这种热情极具感染力。我最欣赏的是它对于“问题”本身的呈现方式。书中提出的很多问题，它们并没有一开始就告诉你解决方案，而是通过层层铺垫，让你自己去思考，去尝试，去感受解决问题的过程。这种“引导式”的学习方式，比直接给出答案更能激发人的学习兴趣和解决问题的能力。有时候，我会遇到一个棘手的问题，在书中作者会给出一些提示，这些提示往往非常巧妙，既不会直接透露答案，又能让你茅塞顿开。那种“原来如此”的瞬间，是学习数学最美妙的体验之一。我记得有一个关于几何的问题，我卡了很久，尝试了各种方法都不得其解。当我读到书中关于这个问题的讲解时，我才恍然大悟，原来解决的关键在于一个简单的视角转换。这种“化繁为简”的智慧，正是这本书的魅力所在。此外，书中选取的“数学珍宝”也十分精妙，它们跨越了不同的数学领域，从基础的数论到更复杂的组合数学，甚至触及了一些代数和几何的奥秘。这种广度让我得以领略到数学的博大精深，而每一种“珍宝”的打磨都极其细腻，让你能品味到其背后的深刻内涵。这本书的语言风格也十分独特，既有严谨的数学论述，又不失趣味性和人文关怀。作者仿佛在与你进行一场心与心的对话，分享他对数学世界的独到见解。我常常在睡前阅读这本书，那些优美的数学论证和深刻的洞察，总能给我带来一种宁静而满足的思考。它让我意识到，数学并非冷冰冰的公式和定理，而是一个充满创造力和想象力的艺术世界。
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