Geometric Studies in Combinatorial Mathematics

Alexander Soifer, How Does One Cut a Triangle?

Boltyanski and Soifer have titled their monograph aptly, inviting talented students to develop their technique and understanding by grappling with a challenging array of elegant combinatorial problems having a distinct geometric tone. The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art . . .
Keep this book at hand as you plan your next problem solving seminar.


in The American Mathematical Monthly Geometric Etudes shows geometry in a refreshing light as a subject whose frontiers are approachable by students of a range of abilities. Portions of the book are appropriate for all students, whereas other sections challenge the best students and hone both their problem-solving abilities and their ingenuity. I strongly recommend this book as a source for interesting, nonstandard geometry problems.


in The Mathematics Teacher This interesting and delightful book by two well-known geometers is written both for mature mathematicians interested in somewhat unconventional geometric problems and especially for talented young students who are interested in working on unsolved problems which can be easily understood by beginners and whose solutions perhaps will not require a great deal of knowledge but may require a great deal of ingenuity . . . I recommend this book very warmly.


Alexander Soifer and Vladimir Boltyanski have produced a fascinating book, filled with material I have not seen before in any book.


Throughout the text, the authors show great mastery of the topics discussed. Their infectious enthusiasm for opening our eyes to the beauties of the worlds of geometry and combinatorics should make this book attractive to a wide audience. It is to be hoped that the following pages will bring the joy of understanding, seeing, and discovering geometry to many of our young people.


This is a popular book written for talented high school students. Also a mathematician can get much pleasure in recalling some well known theorems and problems on tilings, graphs, and most of all on convex figures. Very many exercises with solutions are built into the text. This gives some extra pleasure to the reader and enables to draw him into an active study.


in Zentralblatt fur Mathematik . . . The reader is surprised and delighted by exquisite gems of geometry and combinatorics. A leisurely and captivating presentation leads the reader into a world of tilings, graphs, and convex figures. It is a world that will be long remembered for its striking problems and results.