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Mathemagical Buffet
Mathemagical Buffet offers a delectable feast to everyone with a basic facility in secondary-school mathematics. Every topic reflects the incomparable excitement, beauty, and joy of mathematics; they present a wealth of ingenious insights and marvelous ideas at the fundamental level.
The chapters are independent and can be read in any order. Everyone who enjoys elementary mathematics will truly delight in the following gems:
｜． Pythagorean Triples via Geometry ｜．New proofs of Generalizations of the Theorems of Ptolemy and Simson ｜． Mind Reading Tricks, Ladder Lotteries, Mazes, Lattice Points, Round Robin Competitions, An Elementary Fixed Point Theorems and More ｜．Simple proofs of the lovely Theorems of Pick and of Jung ｜．The Constructibility of a Regular 17-gon ｜．Open Problems on Egyptian Fractions and on Primes
Moreover, the reader is gently encouraged to participate actively by responding to a line of questions that are thoughtfully sprinkled throughout the developments of the expositions.
The chapters are independent and can be read in any order. Everyone who enjoys elementary mathematics will truly delight in the following gems:
｜． Pythagorean Triples via Geometry ｜．New proofs of Generalizations of the Theorems of Ptolemy and Simson ｜． Mind Reading Tricks, Ladder Lotteries, Mazes, Lattice Points, Round Robin Competitions, An Elementary Fixed Point Theorems and More ｜．Simple proofs of the lovely Theorems of Pick and of Jung ｜．The Constructibility of a Regular 17-gon ｜．Open Problems on Egyptian Fractions and on Primes
Moreover, the reader is gently encouraged to participate actively by responding to a line of questions that are thoughtfully sprinkled throughout the developments of the expositions.
- Preface
- 1 Sums of Consecutive Integers
- 2 Galilean Ratios
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3 The Pythagorean Theorem
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3.1 Proofs
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3.2 A Puzzle
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3.3 Pythagorean Triples
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3.4 Generalizations of the Pythagorean Theorem
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4 Japanese Temple Mathematics
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4.1 Problems
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4.2 Solutions
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5 Mind Reading Tricks
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5.1 Trick 1
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5.2 Trick 2
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6 Magic Squares
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6.1 New Year Puzzle 2010
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6.2 Magic Squares
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7 Fun with Areas
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7.1 Two Theorems of Newton
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7.2 A Charming Construction Problem
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7.3 A Generalization of the Simson Theorem
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- 8 The Tower of Hanoi
- 9 Ladder Lotteries
- 10 Round Robin Competitions
- 11 Egyptian Fractions
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12 The Ptolemy Theorem
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12.1 The Ptolemy Theorem
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12.2 Applications
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12.3 A Generalization of the Ptolemy Theorem
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13 Convexity
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13.1 Introduction
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13.2 The Theorems of Jung and Helly
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14 The Seven Bridges of Konigberg
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14.1 Unicursal Figures
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14.2 Mazes
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15 The Euler Formula
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15.1 The Euler Formula
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15.2 Regular Polyhedra
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16 The Sperner Lemma
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16.1 The Sperner Lemma
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16.2 The Brouwer Fixed Point Theorem
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16.3 An Elementary Fixed Point Theorem
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17 Lattice Points
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17.1 The Pick Theorem
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17.2 Lattice Equilateral Triangle
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17.3 Lattice Equiangular Polygons
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17.4 Lattice Regular Polygons
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18 The Sums of Special Series
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18.1 The Sum of the Powers
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18.2 The Binomial Coe cients
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18.3 Faulhaber Polynomials
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18.4 The Sums of the Reciprocals of Sp(n)
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18.5 The Sums of Trigonometric Functions
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- 19 The Morley Theorem
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20 Angle Trisection
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20.1 Rules of Engagement
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20.2 The Trisection Equation
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20.3 Computations by Straightedge and Compass
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20.4 Fields and their Extensions
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20.5 Impossibility Proofs
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20.6 Bending of the Rules
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20.7 Regular Polygons
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20.8 Regular 17-gon
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- 21 Conics
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22 Primes
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22.1 Number of Primes
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22.2 An Open Problem
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23 Gaussian Integers
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23.1 Gaussian Primes
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23.2 An Application to Real Primes
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- 24 Calculus with Complex Numbers
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Appendix Determinants
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A.1 Genesis
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A.2 Properties
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A.3 The Laplace Expansion Theorem
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- 出版地 ： 臺灣
- 語言 ： 英文
- DOI ： 10.6327/NTUPRS-9789860355109
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