Ross Hosnberger
Mathematical Association of America (MAA) | The Dolciani Mathematical Expositions Vol. 9 | 1985 | 250 páginas | DjVu | 2 MB
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Ross Honsberger is the author of six books published in the Dolciani
Mathematical Expositions Series, each of which presents problems from
algebra, arithmetic, number theory, probability, and geometry, and
provides us with an ingenious solution to those problems. His most
recent addition to the Dolciani series is: "More Mathematical Morsels"
which is a continuation of the earlier "Mathematical Morsels" volume
published in 1979. The problems presented here are meant to be enjoyed,
rather than instruct, although instruction is almost always the
automatic by-product. All of the problems in this collection are
concerned only with elementary problems, but each of them contains
something exciting - a surprising result, an intriguing approach, a
stroke of ingenuity.
CONTENTS
CHAPTER PAGE
1. Gleanings from Combinatorics 1
2. Gleanings from Geometry 18
3. Two Problems in Combinatorial Geometry 36
4. Sheep Fleecing with Walter Funkenbusch 48
5. Two Problems in Graph Theory 56
6. Two Applications of Generating Functions 64
7. Some Problems from the Olympiads 76
8. A Second Look at the Fibonacci and Lucas Numbers 102
9. Some Problems in Combinatorics 139
10. Four Clever Schemes in Cryptography 151
11. Gleanings from Number Theory 174
12. Schur's Theorem; An Application of Ramsey's Theorem 183
13. Two Applications of Helly's Theorem 186
14. An Introduction to Ramanujan's Highly Composite Numbers 193
15. On Sets of Points in the Plane 201
16. Two Surprises from Algebra 208
17. A Problem of Paul Erdos 215
18. Cai Mao-Cheng's Solution to Katona's Problem
on Families of Separating Subsets 224
Solutions to Selected Exercises 241
Glossary 247
Index 249
