<P>　　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.</P>
<P>　　The chapters are independent and can be read in any order. Everyone who enjoys elementary mathematics will truly delight in the following gems:</P>
<P>　　l． Pythagorean Triples via Geometry<BR>　　l．New proofs of Generalizations of the Theorems of Ptolemy and Simson<BR>　　l． Mind Reading Tricks, Ladder Lotteries, Mazes, Lattice Points, Round Robin Competitions, An Elementary Fixed Point Theorems and More<BR>　　l．Simple proofs of the lovely Theorems of Pick and of Jung<BR>　　l．The Constructibility of a Regular 17-gon<BR>　　l．Open Problems on Egyptian Fractions and on Primes</P>
<P>　　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.</P>
<P><STRONG>作者簡介</STRONG></P>
<P>　　Liong-shin Hahn was born in Tainan, Taiwan. He obtained his B.S. from the National Taiwan University, and his Ph.D. from Stanford University. 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 (National Taiwan University Press, 2012), 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.</P><P>Preface　ix</P>
<P><STRONG>1 Sums of Consecutive Integers　1</STRONG></P>
<P><STRONG>2 Galilean Ratios　7</STRONG></P>
<P><STRONG>3 The Pythagorean Theorem　11<BR></STRONG>　3.1 Proofs　11<BR>　3.2 A Puzzle　17<BR>　3.3 Pythagorean Triples　18<BR>　3.4 Generalizations of the Pythagorean Theorem　20</P>
<P><STRONG>4 Japanese Temple Mathematics　25<BR></STRONG>　4.1 Problems　25<BR>　4.2 Solutions　27</P>
<P><STRONG>5 Mind Reading Tricks　41<BR></STRONG>　5.1 Trick 1　41<BR>　5.2 Trick 2　43</P>
<P><STRONG>6 Magic Squares　47<BR></STRONG>　6.1 New Year Puzzle 2010　47<BR>　6.2 Magic Squares　49</P>
<P><STRONG>7 Fun with Areas　53<BR></STRONG>　7.1 Two Theorems of Newton　53<BR>　7.2 A Charming Construction Problem　59<BR>　7.3 A Generalization of the Simson Theorem　62</P>
<P><STRONG>8 The Tower of Hanoi　67</STRONG></P>
<P><STRONG>9 Ladder Lotteries　71</STRONG></P>
<P><STRONG>10 Round Robin Competitions　79</STRONG></P>
<P><STRONG>11 Egyptian Fractions　83</STRONG></P>
<P><STRONG>12 The Ptolemy Theorem　89<BR></STRONG>　12.1 The Ptolemy Theorem　89<BR>　12.2 Applications　90<BR>　12.3 A Generalization of the Ptolemy Theorem　92</P>
<P><STRONG>13 Convexity 95<BR></STRONG>　13.1 Introduction　95<BR>　13.2 The Theorems of Jung and Helly　96</P>
<P><STRONG>14 The Seven Bridges of Konigberg　99<BR></STRONG>　14.1 Unicursal Figures　99<BR>　14.2 Mazes　101</P>
<P><STRONG>15 The Euler Formula　105<BR></STRONG>　15.1 The Euler Formula　105<BR>　15.2 Regular Polyhedra108</P>
<P><STRONG>16 The Sperner Lemma　111<BR></STRONG>　16.1 The Sperner Lemma　111<BR>　16.2 The Brouwer Fixed Point Theorem　117<BR>　16.3 An Elementary Fixed Point Theorem　119</P>
<P><STRONG>17 Lattice Points　125<BR></STRONG>　17.1 The Pick Theorem　125<BR>　17.2 Lattice Equilateral Triangle　133<BR>　17.3 Lattice Equiangular Polygons　135<BR>　17.4 Lattice Regular Polygons　138</P>
<P><STRONG>18 The Sums of Special Series　139<BR></STRONG>　18.1 The Sum of the Powers　139<BR>　18.2 The Binomial Coe cients　141<BR>　18.3 Faulhaber Polynomials　143<BR>　18.4 The Sums of the Reciprocals of Sp(n)　150<BR>　18.5 The Sums of Trigonometric Functions　153</P>
<P><STRONG>19 The Morley Theorem　157</STRONG></P>
<P><STRONG>20 Angle Trisection　163<BR></STRONG>　20.1 Rules of Engagement　163<BR>　20.2 The Trisection Equation　167<BR>　20.3 Computations by Straightedge and Compass　169<BR>　20.4 Fields and their Extensions　172<BR>　20.5 Impossibility Proofs　176<BR>　20.6 Bending of the Rules　180<BR>　20.7 Regular Polygons　181<BR>　20.8 Regular 17-gon　185</P>
<P><STRONG>21 Conics　195</STRONG></P>
<P><STRONG>22 Primes　203<BR></STRONG>　22.1 Number of Primes　203<BR>　22.2 An Open Problem　205</P>
<P><STRONG>23 Gaussian Integers　209<BR></STRONG>　23.1 Gaussian Primes　209<BR>　23.2 An Application to Real Primes　216</P>
<P><STRONG>24 Calculus with Complex Numbers　219</STRONG></P>
<P>Appendix Determinants　223<BR>　A.1 Genesis　223<BR>　A.2 Properties　232<BR>　A.3 The Laplace Expansion Theorem　235</P>