Mathematical Diamonds (Dolciani Mathematical Expositions)

Ross Honsberger has done it again. He has brought together another wonderful collection of elementary mathematical problems and their solutions abounding in striking surprises and brilliant ideas that reflect the beauty of mathematics. Many of these problems come from mathematical journals. Others come from various mathematical competitions such as the Tournament of the Towns, the Balkan Olympiad, the American Invitational Mathematics Exam, and the Putnam exam. And, of course, there is a problem suggested by Paul Erdös. This book is ideal for students, teachers and anyone interested in recreational mathematics. Preface ......Page 7 Table of Contents ......Page 9 Section 1: The Remarkable Wine-Rack Property......Page 11 Section 2: The Restless Lion......Page 15 Section 3: Apples and Sticks* ......Page 19 Section 4: A Surpising Result of Paul Erdos*......Page 23 Section 5: Miscellaneous Gleanings......Page 29 Section 6: An Application of Thran's Theorem* ......Page 45 Section 7: Four Problems from Putnam Papers......Page 53 Section 8: Topics Based on Problems from Quantum......Page 59 Section 9: Two Distinguished Integers*......Page 89 Section 10: A Property of the Binomial Coefficients*......Page 93 Section 11: Nine Miscellaneous Problems......Page 97 Section 12: A Problem in Coin-Tossing*......Page 113 Section 13: Semi-regular Lattice Polygons*......Page 119 Section 14: Six Problems from the Canadian OpenMathematics Challenge......Page 127 Section 15: Three Pretty Theorems in Geometry......Page 135 Section 16: Two Gems from Euclidean Geometry*......Page 145 Section 17: The rhue-Morse-Hedlund Sequence......Page 153 Section 18: Two Miscellaneous Problems......Page 161 Section 19: A Surprising Property of Regular Polygons......Page 167 Section 20: Three Short Stories in Number Theory*......Page 173 Section 21: Three Geometry Problems......Page 179 Section 22: Three Problems From The 1990Balkan Olympiad......Page 185 Section 23: A Japanese "Fan" Problem......Page 191 Section 24: Slicing a Doughnut......Page 197 Section 25: A Problem from the 1980 Tournamentof the Towns......Page 205 More Challenges......Page 213 Solutions To The Challenges1.......Page 219 Index of Publications......Page 247 Subject Index......Page 249 Geometry and Combinatorial Geometry......Page 250 Algebra, Number Theory, and Probability......Page 251 General Index......Page 253 1. The Remarkable Wine-rack Property. -- 2. The Restless Lion. -- 3. Apples And Sticks. -- 4. A Surprising Result Of Paul Erdʺos. -- 5. Miscellaneous Gleanings. -- 6. An Application Of Turán's Theorem. -- 7. Four Problems From Putnam Papers. -- 8. Topics Based On Problems From Quantum. -- 9. Two Distinguished Integers. -- 10. A Property Of The Binomial Coefficients. -- 11. Nine Miscellaneous Problems. -- 12. A Problem In Coin-tossing. -- 13. Semi-regular Lattice Polygons. -- 14. Six Problems From The Canadian Open Mathematics Challenge. -- 15. Three Pretty Theorems In Geometry. -- 16. Two Gems From Euclidean Geometry. -- 17. The Thue-morse-hedlund Sequence. -- 18. Two Miscellaneous Problems. -- 19. A Surprising Property Of Regular Polygons. -- 20. Three Short Stories In Number Theory. -- 21. Three Geometry Problems. -- 22. Three Problems From The 1990 Balkan Olympiad. -- 23. A Japanese 'fan' Problem. -- 24. Slicing A Doughnut. -- 25. A Problem From The 1980 Tournament Of The Towns. Ross Honsberger. Includes Indexes. Ross Honsberger Has Done It Again. He Has Brought Together Another Wonderful Collection Of Elementary Mathematical Problems And Their Solutions Abounding In Striking Surprises And Brilliant Ideas That Reflect The Beauty Of Mathematics. Many Of These Problems Come From Mathematical Journals. Others Come From Various Mathematical Competitions Such As The Tournament Of The Towns, The Balkan Olympiad, The American Invitational Mathematics Exam, And The Putnam Exam. And, Of Course, There Is A Problem Suggested By Paul Erdos. This Book Is Ideal For Students, Teachers And Anyone Interested In Recreational Mathematics. Ross Honsberg has brought together a collection of elementary mathematical problems with solutions. The book is ideal for students, teachers and general readers