Mathematics is often studied with an air of such seriousness that it doesn't always seem to be much fun. However, it is quite amazing how many surprising results and brilliant arguments one is in a position to enjoy with just a high school background. This is a book of miscellaneous delights, presented not in an attempt to instruct but as a harvest of rewards that are due to good high school students and, of course, those more advanced - their teachers and everyone in the university mathematics community. A half dozen essays are sprinkled among some hundred problems. Many subjects are represented - combinatorics, geometry, number theory, algebra, probability. The sections may be read in any order. The book concludes with twenty-five exercises and their detailed solutions. Something to delight will be found in every section - a surprising result, an intriguing approach, a stroke of ingenuity - and the leisurely pace and generous explanations make the book a pleasure to read.
Author(s): Ross Honsberger
Series: Dolciani Mathematical Expositions #19
Publisher: Mathematical Association of America (MAA)
Year: 1997
Language: English
Pages: 325
Cover
Back Cover
Title
Preface
Contents
Four Engaging Problems
A Problem from the 1991 Asian Pacific Olympiad
Four Problems from the First Round of the 1988 Spanish Olympiad
Problem K797 from Kvant
An Unused Problem from the 1990 International Olympiad
A Problem from the 1990 Nordic Olympiad
Three Problems from the 1991 AIME
An Elementary Inequality
Six Geometry Problems
Two Problems from the 1989 Swedish Olympiad
Two Problems from the 1989 Austrian-Polish Mathematics Competition
Two Problems from the 1990 Australian Olympiad
Problem 1367 from Crux Mathematicorum
Three Problems from Japan
Two Problems from the 1990 Canadian Olympiad
A Problem from the 1989 U. S. A. Olympiad
A Problem on Seating Rearrangements
Three Problems from the 1980 and 1981 Chinese New Year's Contests
A Problem in Arithmetic
A Checkerboard Problem
Two Problems from the 1990 Asian Pacific Olympiad
Four Problems from the 1989 AIME
Five Unused Problems from the 1989 International Olympiad
Five Problems from the 1980 All-Union Russian Olympiad
The Fundamental Theorem of 3-Bar Motion
Three Problems from the 1989 Austrian Olympiad
Three Problems from the Tournament of the Towns Competitions
Problem 1506 from Crux Mathematicorum
Three Unused Problems from the 1987 International Olympiad
Two Problems from the 1981 Leningrad High School Olympiad
Four Problems from the Pi Mu Epsilon Journal—Fall 1992
An Elegant Solution to Morsel 26
Two Euclidean Problems from The Netherlands
Two Problems from the 1989 Singapore Mathematical Society Interschool Competitions
Problem M1046 from Kvant (1987)
Two Theorems on Convex Figures
The Infinite Checkerboard
Two Problems from the 1986 Swedish Mathematical Competition
A Brilliant 1-1 Correspondence
The Steiner-Lehmus Problem Revisited
Two Problems from the 1987 Bulgarian Olympiad
A Problem from the 1987 Hungarian National Olympiad
A Problem from the 1987 Canadian Olympiad
Problem 1123 from Crux Mathematicorum
A Problem from the 1987 AIME
A Generalization of Old Morsel 3
Two Problems from the 1991 Canadian Olympiad
An Old Chestnut
A Combinatorial Discontinuity
A Surprising Theorem of Kummer
A Combinatorial Problem in Solid Geometry
Two Problems from the 1989 Indian Olympiad
A Gem from Combinatorics
Two Problems from the 1989 Asian Pacific Olympiad
A Selection of Joseph Liouville's Amazing Identities Concerning the Arithmetic Functions
A Problem from the 1988 Austrian-Polish Mathematics Competition
An Excursion into the Complex Plane
Two Problems from the 1990 International Olympiad
Exercises
Solutions to the Exercises
