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Mathemagical Cruise

Mathemagical Cruise

  • 統一編號GPN:1011200861
  • 出版日期:2023/08
  • 作/編/譯者:Liong-shin Hahn 著
  • 語言:英文
  • 頁數:252
  • 裝訂:平裝
  • ISBN/ISSN:9789863507543
  • 出版單位:國立臺灣大學
  • 開數:23x17公分
  • 版次:初版
  • 價格:定價$800
書籍介紹

本書不僅收集了有趣的問題及巧妙的解答,更提供了思考與解決問題的絕佳案例。各章節可按任意順序獨立閱讀,藉由巡遊書中蘊藏著各式珍寶的島嶼,讀者將跨越數學的邊界,航行在浩瀚海洋,探索地平線外的無限可能。

目次

Contents
Preface iv
1 Puzzles 1
1.1 Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Double Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 15-Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Klarner’s Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 A Cube Tour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Safe Cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Tilings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.8 A Problem on Weighted Trees . . . . . . . . . . . . . . . . . . . . . 21
2 The Bolyai-Gerwin Theorem 25
2.1 Baby Pythagoras . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 A Triangular Carpet . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 The Bolyai-Gerwin Theorem . . . . . . . . . . . . . . . . . . . . . . 32
3 New Year Puzzles 40
3.1 New Year Puzzle 2014 . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 New Year Puzzle 2015 . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Heron’s Formula Revisited . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 New Year Puzzle 2016 . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 New Year Puzzle 2017 . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.6 New Year Puzzle 2018 . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.7 New Year Puzzle 2019 . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.8 New Year Puzzle 2020 . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.9 New Year Puzzle 2021 . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.10 New Year Puzzle 2022 . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.11 New Year Puzzle 2023 . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.12 New Year Puzzle 2024 . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.13 New Year Puzzle 2025 . . . . . . . . . . . . . . . . . . . . . . . . . 70
iii
iv
4 In Remembrance of Professor Ross Honsberger 72
4.1 The Bulging Semicircle . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2 The Last Digits of 79999 . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 A Diophantine Equation . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Sum of the Digits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Gaps between Consecutive Primes . . . . . . . . . . . . . . . . . . . 76
4.6 Triangle Numbers That Are Perfect Squares . . . . . . . . . . . . . 77
4.7 A Problem by Erd˝os . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Triangles 86
5.1 Medians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2 Orthocenter and Circumcenter . . . . . . . . . . . . . . . . . . . . . 87
5.3 Incenter and Excenters . . . . . . . . . . . . . . . . . . . . . . . . . 91
6 From the Desks of My Friends 97
6.1 From Dean Ballard . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.1.1 What’s a Point in a Square? . . . . . . . . . . . . . . . . . . 97
6.1.2 Wythoff’s Game . . . . . . . . . . . . . . . . . . . . . . . . 106
6.1.3 The Game of Nim . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2 From Tien-Sheng Hsu . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7 How Many Interior Right Angles Can a Polygon Have? 120
8 Ceva and Menelaus Revisited 127
9 Circles 133
9.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.2 Radical Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.3 Coaxal Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
9.4 Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
9.5 Theorems of Ptolemy, Steiner and Poncelet . . . . . . . . . . . . . . 150
9.6 An Old Japanese Theorem . . . . . . . . . . . . . . . . . . . . . . . 156
9.7 With Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10 Lattice Points 162
10.1 The Schinzel Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 162
10.2 Lattice Integer Triangles . . . . . . . . . . . . . . . . . . . . . . . . 168
10.3 The Isbell Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
11 On the Theorems of Simson and of Cantor 186
11.1 The Simson Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 186
A Problems 198
B Solutions and Hints 206

編/著/譯者簡介

Liong-shin Hahn was born in Tainan, Taiwan. After graduating from the Tainan First Middle School and the National Taiwan University, he attended Stanford University and obtained his Ph.D. under Professor Karel deLeeuw. He authored Complex Numbers and Geometry (Mathematical Association of America, 1994), New Mexico Mathematics Contest Problem Book (University of New Mexico Press, 2005), Honsberger Revisited (NTUP, 2011), Mathemagical Buffet (NTUP, 2013), and co-authored with Bernard Epstein Classical Complex Analysis (Jones and Bartlett, 1996). He was awarded the Citation for Public Service from the American Mathematics Society in 1998. His number one hobby is creating/solving mathematical puzzles.

分類 其他詳細資訊
  • 適用對象:成人(學術性)
  • 關鍵詞:mathematical game, elementary mathematics, elementary number theory
  • 附件:無附件
  • 頁/張/片數:252
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