Mathemagical Cruise
Liongshin Hahn
 PublishedAugust, 2023
 Binding平裝 / 23*17 / 248pages / 單色（黑） / 英文
 Publisher國立臺灣大學出版中心
 SeriesEducation－Textbooks
 ISBN9789863507543
 GPN1011200861
 Price NT$800

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 EISBN(PDF)9789863507611
 EISBN(EPub)9789863507604
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Mathemagical Cruise is not a mere collection of fun problems with clever solutions. It offers shining examples of how to approach problem solving.
Each chapter is independent and can be read in any order by everyone with a basic background in high school mathematics. Some highlights of the excursion are:
● Slick Solutions of Double Sequence, Klarner’s Puzzle, Cube Tour, etc.
● Easy Proofs of BolyaiGerwin Theorem, Problem by P. Erdös and more
● New Year Puzzles (Especially, Year 2021 & 2022)
● Twelve Points on the NinePoint Circle
● What's a Point in a Square?
● Five Circles through a 5x6 Grid
● Generalization of Ceva's Theorem
● Easy Approach to Coaxal Circles
● Inversion and its Applications
● Lattice Integer Triangles
● Isbell's Problem
● Sequence of Theorems of Simson & Cantor
● Miscellaneous Problems with Solutions
By cruising through these treasure islands, the reader will traverse mathematical boundaries. Be adventurous and inspired to explore the seas beyond the horizon.
Preface
1 Puzzles
1.1 Parity
1.2 Double Sequences
1.3 15Puzzle
1.4 Klarner’s Puzzle
1.5 A Cube Tour
1.6 Safe Cracking
1.7 Tilings
1.8 A ProblemonWeighted Trees
2 The BolyaiGerwin Theorem
2.1 Baby Pythagoras
2.2 A Triangular Carpet
2.3 The BolyaiGerwin Theorem
3 New Year Puzzles
3.1 New Year Puzzle 2014
3.2 New Year Puzzle 2015
3.3 Heron’s Formula Revisited
3.4 New Year Puzzle 2016
3.5 New Year Puzzle 2017
3.6 New Year Puzzle 2018
3.7 New Year Puzzle 2019
3.8 New Year Puzzle 2020
3.9 New Year Puzzle 2021
3.10 New Year Puzzle 2022
3.11 New Year Puzzle 2023
3.12 New Year Puzzle 2024
3.13 New Year Puzzle 2025
4 In Remembrance of Professor Ross Honsberger
4.1 The Bulging Semicircle
4.2 The Last Digits of 79999
4.3 A Diophantine Equation
4.4 Sumof the Digits
4.5 Gaps between Consecutive Primes
4.6 Triangle Numbers That Are Perfect Squares
4.7 A Problemby Erdӧs
5 Triangles
5.1 Medians
5.2 Orthocenter and Circumcenter
5.3 Incenter and Excenters
6 From the Desks of My Friends
6.1 FromDean Ballard
6.1.1 What’s a Point in a Square?
6.1.2 Wythoff’s Game
6.1.3 The Game of Nim
6.2 From TienSheng Hsu
7 How Many Interior Right Angles Can a Polygon Have?
8 Ceva and Menelaus Revisited
9 Circles
9.1 Preliminaries
9.2 Radical Axes
9.3 Coaxal Circles
9.4 Inversion
9.5 Theorems of Ptolemy, Steiner and Poncelet
9.6 An Old Japanese Theorem
9.7 With Coordinates
10 Lattice Points
10.1 The Schinzel Theorem
10.2 Lattice Integer Triangles
10.3 The Isbell Problem
11 On the Theorems of Simson and of Cantor
Appendix A Problems
Appendix B Solutions and Hints