This book is a monograph on newly created and solved problems in combinatorial geometry. Many of the problems involve dissections of triangles and other geometric figures. The book is intended to show young talented people what mathematics is and what mathematicians do.
Excerpts from the book (tbs)
Preface
Table of Contents
Sample page of problems (pdf)
Sample page of solutions (pdf)
1990 $35.00 140 pages paperback
5 3/4" x 8 1/4"
ISBN 0-940263-01-7
LCCN 90-060349 publisher: CEME
Promotional Material (tbs)
Flyer (pdf)
About the authors
Recommend this book to your library (pdf)
What the reviewers say
Murray S. Klamkin from The American Mathematical Monthly, 98(1991)775-778
"I like the style of the book."
"There is quite a number of unsolved problems which will challenge professional mathematicians and other scientists."
James N. Boyd from the Mathematics Teacher
"Soifer's work can rightly be called a 'mathematical gem.' "
Paul L. Campbell from Mathematics Magazine, 65(1992)139
"Formulates and explores ways to solve new and engaging problems about cutting a triangle into congruent or similar triangles, gradually refining the problems and drawing the reader into the solutions."
V. G. Boltyanski from SIAM Review
"Alexander Soifer has produced a good gift for the young lover of mathematics. And not only for youngsters; the book should be interesting even to professional mathematicians."
Paul Erdös from the Introduction
"This delightful book considers and solves many problems in dividing triangles into n congruent pieces and also into similar pieces, as well as many extremal problems about placing points in convex figures. The book is primarily meant for clever high school students and college students interested in geometry, but even mature mathematicians will find a lot of new material in it. I very warmly recommend the book and hope the readers will have pleasure in thinking about the unsolved problems and will find new ones."
H. A. ShahAli on Amazon.com
"A Geometric Gem."
L. M. Kelley in Mathematical Reviews
"The manner of presentation and the gentle guidance toward a solution and hence to generalizations and new problems takes this elementary treatise out of the prosaic and into the stimulating realm of mathematical creativity. Not only young talented people but dedicated secondary teachers and even a few mathematical sophisticates will find this reading both pleasant and profitable."
Cecil Rousseau from the Introduction
"It reads like an adventure story. In fact, it is an adventure story, complete with interesting characters, moments of exhilaration, examples of serendipity, and unanswered questions. It conveys the spirit of mathematical discovery and it celebrates the event as have mathematicians throughout history."
John Baylis from The Mathematical Gazette, 75(1991)224-225
"Alexander Soifer is a wonderful problem solver and inspiring teacher. His book will tell young mathematicians what mathematics should be like, and remind older ones who may be in danger of forgetting."
"It is such a refreshing book. Professor Soifer makes the problems fascinating, the methods of attack even more fascinating, and the whole thing is enlivened by anecdotes about the history of the problems, some of their recent solvers, and the very human reactions of the author to some beautiful mathematics. Most of all, the book has charm, somehow enhanced by his slightly eccentric English, sufficient to carry the reader forward without minding being asked to do rather a lot of work."
Philip L. Engel from the Introduction
"How does one describe a mathematician? I know no better way than to read this delightful book."
Branko Grünbaum from the Introduction
"[This book is] apt to bring pleasure to anybody willing to devote a few hours to follow its adventures among solved and unsolved problems."
Bill Young on Amazon.com
"Exceptional book!"
"The explanations of the problems are exceptional."