具體描述
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.”
作者簡介
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
圖書目錄
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
圖書序言
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.
中文說明
本書(中譯名：重訪亨斯貝爾格--磨亮數學寶石)是美國 New Mexico 大學退休教授 Liong-Shin Hahn（韓良信）從著名數學傢 Ross A Hongsberger 所著的五本書中選齣好題目，加以探索、分析、解題、延伸之後，寫下的一本「讀數」劄記。
Hongsberger 的這五本書分彆是(1) Mathematical Delights(2004齣版) (2) In Polya's Footsteps(1997齣版) (3) Mathematical Chestnuts from around the world(2001齣版) (4) Mathematical Diamonds(2003齣版) (5) From Erd?s to Kiev(1996齣版)。
韓教授將上述這五本書的書名作為本書的章名，每一章的題目都是從 Hongsberger 對應的書中挑齣來的，並且提供瞭比原書更好，更精緻，且更具啓發性的解法。作者特彆強調「重訪」這本書完全可以獨立閱讀，當然也可以與 Hongsberger 的原書平行閱讀。
除瞭上述五章本文之外，「重訪」一書另有A、B、C三個附錄。附錄A收集瞭115個挑戰題，粗分為52題幾何題，20題代數題，18題數論題，20題組閤題和5題微積分題，解題所需的工具是高中數學。
附錄B是對附錄A的詳解。附錄C是整本「重訪」一書解題所需的定理，作者將這些定理作瞭很好的證明和延伸，這些定理包含瞭中學教育最核心的議題：
c.1 三角形相關定理
c.2 圓形相關定理
c.3 三角學相關定理
c.4 圓錐麯綫相關定理
c.5 Jensen不等式的各種麵貌
本書不單是一本解題手冊，而是藉解題來呈現作者認為最重要的數學，適閤對數學有興趣的高中生、大學生以及中學的數學教師研讀。
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.
圖書試讀
用戶評價
我必須說，在讀完《Honsberger Revisited：Mathematical Gems Polished》之後，我的數學觀被徹底顛覆瞭。我一直以為數學是那些嚴謹、刻闆、隻存在於書本上的抽象概念，但這本書徹底打破瞭我的刻闆印象。它以一種極其生動、富有啓發性的方式，將那些隱藏在日常生活和社會中的數學規律和美感揭示齣來。我尤其喜歡書中對於“巧思”的強調。很多時候，解決一個數學難題的關鍵，不在於你掌握瞭多少復雜的公式，而在於你是否能找到一個巧妙的角度，或者一個簡單的邏輯。這本書就像是一個寶庫，裏麵陳列著無數這樣的“巧思”，它們如同精美的藝術品，讓人贊嘆不已。例如，書中有一個關於排列組閤的問題，看似復雜，但作者通過一個簡單的模型，就將其變得清晰明瞭。我當時就有一種豁然開朗的感覺，後悔自己之前為什麼沒有想到這一點。這種“頓悟”的時刻，是學習過程中最令人興奮的體驗。這本書的結構設計也非常閤理，每一個“數學珍寶”都被獨立地呈現齣來，但又相互關聯，形成瞭一個有機整體。你可以按照自己的節奏來閱讀，或者跳讀你感興趣的部分。我個人傾嚮於逐章閱讀，這樣更能感受到作者循序漸進的引導，以及數學概念之間的內在聯係。書中那些精美的插圖和圖錶，更是錦上添花，它們不僅僅是為瞭說明問題，更是將抽象的數學概念可視化，讓你更容易理解和記憶。我記得有一個關於不動點定理的講解，書中用瞭一個生動的例子，並配以精美的圖示，讓我一下子就理解瞭那個曾經睏擾我的定理。這不僅僅是一本學習數學的書，更是一本激發思考、培養創意的書。它讓我看到瞭數學在各個領域的應用，也讓我對數學的未來充滿瞭無限的憧憬。
评分《Honsberger Revisited：Mathematical Gems Polished》這本書，對於我來說，不僅僅是一本關於數學的書，更是一次與智者對話的經曆。它以一種獨特的方式，將那些曾經令我感到遙不可及的數學概念，變得鮮活而生動。我特彆喜歡書中那種“循循善誘”的講解風格。作者並沒有直接告訴你答案，而是引導你一步步地去思考，去探索，去發現。這種“自己動手”的解決問題的過程，讓我更加深刻地理解瞭數學的本質。我印象最深刻的是書中一個關於“鴿籠原理”的講解。作者通過一個生動的例子，讓我一下子就明白瞭“鴿籠原理”的精妙之處。那種“豁然開朗”的感覺，是任何一種死記硬背都無法給予的。此外，書中那些“數學的趣味性”的呈現，更是讓我驚喜連連。作者在講解數學問題的過程中，會穿插一些有趣的謎題和悖論，讓整個學習過程變得更加輕鬆愉快。我甚至在閱讀過程中，會時不時地和傢人朋友討論書中的內容，分享我的學習心得。這種交流和分享，讓我更加鞏固瞭對知識的理解。這本書的排版設計也十分考究，文字清晰，圖錶精美，給人一種賞心悅目的感覺。我甚至會反復翻閱書中的一些插圖，試圖從中發現更多的數學信息。總而言之，這是一本能夠讓你在享受閱讀樂趣的同時，大幅提升數學思維能力的書。它不僅能夠拓展你的知識維度，更重要的是，它能夠培養你對數學的熱情和好奇心。
评分當我拿到《Honsberger Revisited：Mathematical Gems Polished》這本書時，我並沒有抱有太高的期望，畢竟數學普及類的書籍琳琅滿目，能真正觸動人心的並不多。然而，這本書卻給瞭我一個巨大的驚喜。它以一種極為巧妙的方式，將那些深奧的數學概念，轉化為一個個引人入勝的故事和問題。我並非數學科班齣身，但這本書的講解方式，讓我能夠輕鬆地理解那些原本可能令人望而卻步的數學知識。作者仿佛是一位經驗豐富的嚮導，他並沒有強迫你一次性接受所有信息，而是耐心地引導你，讓你在自己的節奏下，慢慢地領略數學的魅力。我最欣賞的是書中對於“反常識”的數學現象的介紹。很多時候，我們直覺上的判斷在數學的世界裏是行不通的，而這本書就善於揭示這些“反常識”之處，讓你不禁感嘆數學的神奇。我記得書中有一個關於概率的問題，它挑戰瞭我一直以來的認知，讓我對隨機事件有瞭全新的理解。這種“顛覆認知”的體驗，是學習過程中最寶貴的財富之一。這本書的敘述語言十分優雅，既有學術的嚴謹，又不失文學的韻味。作者在講解數學問題的過程中，會穿插一些曆史故事和名人軼事，讓整個學習過程變得更加生動有趣。我甚至在閱讀過程中，會不自覺地被作者的文筆所吸引，仿佛在品讀一本優秀的散文集。這本書的裝幀設計也十分精美，紙張的觸感和墨水的味道，都傳遞齣一種高品質的閱讀體驗。我常常會把這本書放在床頭，睡前翻幾頁，讓數學的智慧陪伴我入眠。總而言之，這是一本能夠讓你在輕鬆愉快的氛圍中，提升數學素養的書。它不僅能夠拓展你的知識麵，更重要的是，它能夠激發你對數學的興趣，讓你看到數學的無限可能。
评分我必須承認，《Honsberger Revisited：Mathematical Gems Polished》這本書，在我沉寂已久的數學熱情中，點燃瞭一簇新的火焰。我曾一度認為，數學隻是枯燥的公式和抽象的符號，但這本書徹底改變瞭我的看法。它用一種極其富有感染力的方式，將數學的“美”和“趣味”展現在我麵前。我尤其喜歡書中對“數學思維”的強調。很多時候，一個看似復雜的問題，可能隻需要一個簡單的數學思想，就能迎刃而解。這本書就像是一本“思維寶典”，裏麵蘊含著無數解決問題的“絕招”。我記得書中有一個關於整數分拆的問題，我之前嘗試瞭各種方法都無從下手。當讀到書中作者提供的“生成函數”的思路時，我纔豁然開朗，那種“原來如此”的驚喜，至今難忘。這種“點石成金”的智慧，正是這本書的魅力所在。作者的敘述風格也非常流暢，他善於將復雜的數學概念，用通俗易懂的語言進行解釋，同時又不失其深刻內涵。我常常在閱讀過程中，會不自覺地跟著作者的思路一起思考，仿佛在進行一場有趣的頭腦風暴。這本書的排版設計也十分齣色，文字清晰，圖錶精美，給人一種高雅而舒適的閱讀感受。我甚至會反復翻閱書中的一些圖示，試圖從中發現更多的數學細節。總而言之，這是一本能夠讓你在享受閱讀樂趣的同時，大幅提升數學能力的著作。它不僅能夠拓展你的知識邊界，更重要的是，它能夠讓你領略到數學作為一門藝術的魅力。
评分《Honsberger Revisited：Mathematical Gems Polished》這本書，在我看來，是一次對數學本質的深刻挖掘與優雅呈現。它不像許多泛泛而談的科普讀物，而是精選瞭一係列具有代錶性的“數學珍寶”，並對其進行瞭細緻入微的打磨。我特彆喜歡書中對每一個“珍寶”的介紹方式，它不是簡單地羅列公式和定理，而是從一個具體的問題齣發，引導讀者逐步走嚮深刻的數學洞察。這種“由果溯因”的講解模式，讓我更能理解數學知識的由來和應用。我印象最深刻的是書中一個關於圖論的例子。作者通過一個簡單的城市交通網絡問題，巧妙地引入瞭圖論的概念，並展示瞭如何用數學工具來解決實際問題。這個例子讓我對圖論産生瞭濃厚的興趣，也讓我認識到數學並非遙不可及，而是與我們的生活息息相關。這本書的語言風格非常獨特，既有數學的嚴謹性，又不乏幽默感。作者在解釋復雜概念時，經常會運用形象的比喻和生動的類比，讓我能夠更容易地理解和記憶。我甚至在閱讀過程中，會時不時地會心一笑，被作者的幽默所感染。這種寓教於樂的學習方式，是我非常看重的。此外，書中那些精美的插圖和數學模型，更是為整個閱讀體驗增色不少。它們不僅僅是文字的輔助，更是將抽象的數學概念具象化，讓我能夠更直觀地感受到數學的美。我經常在閱讀時，一邊對照圖錶，一邊跟著作者的思路推導，這種沉浸式的學習體驗，讓我受益匪淺。總而言之，這是一本能夠讓你在不知不覺中，愛上數學的書。它不僅能夠拓展你的數學視野，更重要的是，它能夠培養你獨立思考和解決問題的能力。
评分對於我而言，《Honsberger Revisited：Mathematical Gems Polished》是一次久違的智力冒險，更是一場感官與思維的雙重盛宴。這本書並非市麵上常見的“速成”指南，而是一本需要讀者靜下心來，用心去品味的著作。它就像一位技藝精湛的珠寶匠，將一顆顆未經打磨的數學原石，精心雕琢成閃耀奪目的寶石，然後一件件地展示在讀者麵前。我喜歡書中那種“抽絲剝繭”的講解方式。作者不會急於給齣結論，而是引導你一步步地去探索，去發現。每一個數學問題都像是一個等待被解開的謎團，而作者的敘述，就像是為你點亮瞭前進道路上的火把。我常常在閱讀過程中，一邊跟著作者的思路思考，一邊在腦海中勾勒齣各種可能的解決方案。有時候，我會嘗試自己去推導，去驗證，即使遇到睏難，也不會感到沮喪，反而會更加激發我的鬥誌。因為我知道，最終的答案，一定隱藏在作者的筆下，等待我去發掘。書中那些“數學珍寶”的選取，更是體現瞭作者的獨到眼光。它們不僅僅是那些枯燥的定理和公式，而是那些能夠激發你思考、讓你眼前一亮的數學“妙趣”。我記得有一個關於數論的問題，我之前從未接觸過，但通過作者的講解，我卻能體會到其中蘊含的深刻邏輯和簡潔之美。這種“美的體驗”，是任何一種枯燥的解題練習都無法給予的。這本書的排版和設計也堪稱一流。每一個數學公式都清晰易懂，每一個圖錶都精心繪製，給人一種賞心悅目的感覺。我甚至會反復翻閱書中的圖錶，試圖從中發現更多的細節和信息。總而言之，這是一本值得反復閱讀、反復思考的書。它不僅能夠提升你的數學知識，更重要的是，它能夠培養你對數學的熱愛，以及獨立思考和解決問題的能力。
评分自從我開始閱讀《Honsberger Revisited：Mathematical Gems Polished》這本書以來，我仿佛進入瞭一個全新的數學世界。它不再是那些令人生畏的定理和公式，而是充滿瞭驚喜和發現的奇妙旅程。我最欣賞的是書中對於“數學的優雅”的展現。作者並非簡單地羅列知識點，而是通過精心設計的講解，讓你體會到數學邏輯的精巧和數學結論的美妙。我記得書中有一個關於斐波那契數列的講解，作者從一個簡單的兔子繁殖問題齣發，逐步引齣瞭斐波那契數列的各種神奇性質。這種“層層深入”的講解方式，讓我能夠真正地理解和欣賞這個數列的美。此外，書中那些“意想不到”的數學聯係，更是讓我驚喜連連。作者善於將看似無關的數學概念聯係起來，讓你看到數學的統一性和深刻性。我甚至在閱讀過程中，會時不時地停下來，思考作者提齣的問題，並嘗試自己去尋找答案。這種主動的學習方式，讓我更加深入地理解瞭書中內容。這本書的語言風格也十分簡潔有力，作者用最精煉的語言，錶達瞭最深刻的數學思想。我常常在閱讀時，會被作者的文字所吸引，仿佛在品讀一首優美的詩歌。這本書的裝幀設計也極具藝術感，書的整體風格沉穩而大氣，透露齣一種知識的力量。總而言之，這是一本能夠讓你在享受閱讀樂趣的同時，對數學産生濃厚興趣的書。它不僅能夠拓展你的知識廣度，更重要的是，它能夠培養你發現數學之美的能力。
评分這本書的封麵設計就透著一股沉靜而又充滿智慧的吸引力，深沉的藍色搭配金色的書名，仿佛是在預示著裏麵蘊含著的是經過歲月打磨、光彩奪目的數學珍寶。我是在一個偶然的機會接觸到這本《Honsberger Revisited：Mathematical Gems Polished》的，當時對這個名字就産生瞭濃厚的興趣，“Revisited”暗示著對經典的迴顧和升華，“Mathematical Gems”則明確瞭其內容的核心——那些數學領域中閃耀的、令人驚嘆的寶藏。“Polished”更是點睛之筆，說明這些寶石並非未經雕琢，而是經過精心打磨，以最清晰、最 elegant 的方式呈現給讀者。我的數學背景不算特彆深厚，更多的是一種對未知世界的好奇和探索欲，所以當我翻開這本書時，並沒有抱著要啃下高難度定理的決心，更多的是一種學習和欣賞的心態。我喜歡它那種循序漸進的講解方式，雖然涉及的數學概念可能對於初學者來說有些挑戰，但作者 Honsberger 先生（或者說是這本書的作者團隊，如果不是直接由 Honsberger 本人編寫的話，但無論如何，其精神和風格都被很好地繼承和發揚瞭）的敘述方式非常生動有趣，仿佛一位經驗豐富的嚮導，耐心地引領著我穿越數學的叢林。他善於用直觀的例子和巧妙的比喻來解釋抽象的概念，這一點對我來說至關重要。我經常發現自己在閱讀過程中會不自覺地停下來，反復咀嚼作者的文字，甚至會拿紙筆演算一下，試圖親身體驗那種“aha moment”。這本書不僅僅是知識的堆砌，更是一種思維方式的啓迪。它教會我如何去觀察，如何去分析，如何去尋找問題背後更深層次的結構。即使是那些我之前從未接觸過的數學分支，通過作者的講解，也變得不再那麼令人望而卻步。我尤其喜歡書中那些“未解之謎”或者“待探索的領域”的介紹，它們像是在我麵前打開瞭一扇扇通往更廣闊數學世界的大門，激發瞭我進一步學習的動力。這本書的排版也很精美，插圖和圖錶的運用恰到好處，極大地提升瞭閱讀體驗。總而言之，這是一本我非常願意推薦給任何對數學懷有好奇心的人的書，無論你是數學專業的學生，還是僅僅是對此領域感到興趣的業餘愛好者，都能從中受益匪淺。它不僅僅是一本教科書，更像是一本充滿智慧和啓發的讀物。
评分作為一名多年的數學愛好者，我曾涉獵過不少數學普及讀物，但《Honsberger Revisited：Mathematical Gems Polished》給我的感受絕對是獨一無二的。這本書並非那種填鴨式的知識灌輸，而是以一種非常“親切”的方式，將一個個精巧絕倫的數學問題呈現在讀者麵前。我可以感覺到，作者在字裏行間流露齣的那種對數學的熱愛和對美的追求，這種熱情極具感染力。我最欣賞的是它對於“問題”本身的呈現方式。書中提齣的很多問題，它們並沒有一開始就告訴你解決方案，而是通過層層鋪墊，讓你自己去思考，去嘗試，去感受解決問題的過程。這種“引導式”的學習方式，比直接給齣答案更能激發人的學習興趣和解決問題的能力。有時候，我會遇到一個棘手的問題，在書中作者會給齣一些提示，這些提示往往非常巧妙，既不會直接透露答案，又能讓你茅塞頓開。那種“原來如此”的瞬間，是學習數學最美妙的體驗之一。我記得有一個關於幾何的問題，我卡瞭很久，嘗試瞭各種方法都不得其解。當我讀到書中關於這個問題的講解時，我纔恍然大悟，原來解決的關鍵在於一個簡單的視角轉換。這種“化繁為簡”的智慧，正是這本書的魅力所在。此外，書中選取的“數學珍寶”也十分精妙，它們跨越瞭不同的數學領域，從基礎的數論到更復雜的組閤數學，甚至觸及瞭一些代數和幾何的奧秘。這種廣度讓我得以領略到數學的博大精深，而每一種“珍寶”的打磨都極其細膩，讓你能品味到其背後的深刻內涵。這本書的語言風格也十分獨特，既有嚴謹的數學論述，又不失趣味性和人文關懷。作者仿佛在與你進行一場心與心的對話，分享他對數學世界的獨到見解。我常常在睡前閱讀這本書，那些優美的數學論證和深刻的洞察，總能給我帶來一種寜靜而滿足的思考。它讓我意識到，數學並非冷冰冰的公式和定理，而是一個充滿創造力和想象力的藝術世界。
评分當我捧起《Honsberger Revisited：Mathematical Gems Polished》這本書時，我首先被其沉靜而又充滿智慧的書名所吸引。它仿佛承諾著一場關於數學的探索之旅，而這本書也確實不負眾望。我並非科班齣身的數學專業人士，更多的是對世界運行規律的好奇，而這本書恰好滿足瞭我這種探索欲。它沒有過於艱澀的術語，也沒有高不可攀的理論，而是以一種“潤物細無聲”的方式，將一個個精妙絕倫的數學“寶石”呈現在我眼前。我尤其欣賞書中對於“問題的解構”的處理方式。作者往往會先提齣一個看似簡單，卻又蘊含深刻道理的問題，然後一步步地引導讀者去分析，去思考，去尋找解決問題的鑰匙。這種“引導式”的學習過程，比直接給予答案更能激發人的內在動力。我記得書中有一個關於排列組閤的問題，我之前總是憑感覺去猜測，結果屢屢齣錯。當讀到書中作者用“分類討論”和“排除法”來解決這個問題時，我纔恍然大悟，原來解決問題的關鍵在於清晰的邏輯思路。這種“撥雲見日”的體驗，讓我受益匪淺。此外，書中那些跨越不同數學領域的“連接”，更是讓我看到瞭數學的宏大與統一。作者仿佛一位技藝高超的織匠，將零散的數學知識點，編織成一幅幅精美的畫捲。我甚至在閱讀過程中，會不自覺地將書中的數學思想應用到我的日常思考中。這本書的排版設計也極為用心，文字的疏密有緻，圖錶的精巧繪製，都讓閱讀成為一種享受。總而言之，這是一本能夠讓你在輕鬆愉快的閱讀體驗中，深刻領略數學魅力，並培養獨立思考和解決問題能力的書。
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