eBook ISBN:  9781470457211 
Product Code:  DOL/19.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
eBook ISBN:  9781470457211 
Product Code:  DOL/19.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 

Book DetailsDolciani Mathematical ExpositionsVolume: 19; 1997; 325 pp
Ross Honsberger was born in Toronto, Canada, in 1929 and attended the University of Toronto. After more than a decade of teaching mathe matics in Toronto, he took advantage of a sabbatical leave to continue his studies at the University of Waterloo, Canada. He joined its faculty in 1964 in the Department of Combina torics and Optimization, and has been there ever since.
Honsberger has published a number of bestselling books with the Mathematical Association of America, including Episodes in Nineteenth and Twentieth Century Euclidean Geometry, and From Erdős to Kiev. In Pólya's Footsteps is his eighth book published in the Dolciani Mathematical Exposition Series.
The study of mathematics is often undertaken with an air of such seriousness that it doesn't always seem to be much fun at the time. 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 good high school students and, of course, those more advanced—their teachers, and everyone in the university mathematics community. Admittedly, they take a little concentration, but the price is a bargain for such gems.
A half dozen essays are sprinkled among some hundred problems, most of which are the easier problems that have appeared on various national and international olympiads. Many subjects are represented—combinatorics, geometry, number theory, algebra, probability. The sections may be read in any order. The book concludes with twentyfive exercises and their detailed solutions.
It is hoped that something to delight will be found in every section—a surprising result, an intriguing approach, a stroke of ingenuity—and that the leisurely pace and generous explanations will make them a pleasure to read. The inspiration for many of the problems came from the Olympiad Corner of Crux Mathematicorum, published by the Canadian Mathematical Society.

Table of Contents

Articles

Four Engaging Problems

A Problem from the 1991 Asian Pacific Olympiad

Four Problems from the First Round of the 1988 Spanish Olympiad

Problem K979 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 AustrianPolish 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 Contest

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

Four Geometry Problems

Five Problems from the 1980 AllUnion Russian Olympiad

The Fundamental Theorem of 3Bar 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 11 Correspondence

The SteinerLehmus 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 $\sigma (n)$, $\tau (n)$, $\phi (n)$, $\mu (n)$, $\lambda (n)$

A Problem from the 1988 AustrianPolish Mathematics Competition

An Excursion into the Complex Plane

Two Problems from the 1990 International Olympiad


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
Ross Honsberger was born in Toronto, Canada, in 1929 and attended the University of Toronto. After more than a decade of teaching mathe matics in Toronto, he took advantage of a sabbatical leave to continue his studies at the University of Waterloo, Canada. He joined its faculty in 1964 in the Department of Combina torics and Optimization, and has been there ever since.
Honsberger has published a number of bestselling books with the Mathematical Association of America, including Episodes in Nineteenth and Twentieth Century Euclidean Geometry, and From Erdős to Kiev. In Pólya's Footsteps is his eighth book published in the Dolciani Mathematical Exposition Series.
The study of mathematics is often undertaken with an air of such seriousness that it doesn't always seem to be much fun at the time. 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 good high school students and, of course, those more advanced—their teachers, and everyone in the university mathematics community. Admittedly, they take a little concentration, but the price is a bargain for such gems.
A half dozen essays are sprinkled among some hundred problems, most of which are the easier problems that have appeared on various national and international olympiads. Many subjects are represented—combinatorics, geometry, number theory, algebra, probability. The sections may be read in any order. The book concludes with twentyfive exercises and their detailed solutions.
It is hoped that something to delight will be found in every section—a surprising result, an intriguing approach, a stroke of ingenuity—and that the leisurely pace and generous explanations will make them a pleasure to read. The inspiration for many of the problems came from the Olympiad Corner of Crux Mathematicorum, published by the Canadian Mathematical Society.

Articles

Four Engaging Problems

A Problem from the 1991 Asian Pacific Olympiad

Four Problems from the First Round of the 1988 Spanish Olympiad

Problem K979 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 AustrianPolish 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 Contest

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

Four Geometry Problems

Five Problems from the 1980 AllUnion Russian Olympiad

The Fundamental Theorem of 3Bar 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 11 Correspondence

The SteinerLehmus 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 $\sigma (n)$, $\tau (n)$, $\phi (n)$, $\mu (n)$, $\lambda (n)$

A Problem from the 1988 AustrianPolish Mathematics Competition

An Excursion into the Complex Plane

Two Problems from the 1990 International Olympiad