In Polya's Footsteps : Miscellaneous Problems and Essays 0883853264, 9780883853269
Mathematics is often studied with an air of such seriousness that it doesn't always seem to be much fun. However, i
271 50 2MB
English Pages 325 [329] Year 1997
Table of contents :
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
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
