How Does One Cut a Triangle?

This second edition of Alexander Soifer’s How Does One Cut a Triangle? demonstrates how different areas of mathematics can be juxtaposed in the solution of a given problem. The author employs geometry, algebra, trigonometry, linear algebra, and rings to develop a miniature model of mathematical research.

How Does One Cut a Triangle? contains dozens of proofs and counterexamples to a variety of problems, such as a pool table problem, a fifty-dollar problem, a five-point problem, and a joint problem. By proving these examples, the author demonstrates that research is a collection of mathematical ideas that have been developed throughout the course of history.

The author brings mathematics alive by giving the reader a taste of what mathematicians do. His book presents open problems that invite the reader to play the role of the mathematician. By doing so, the author skillfully inspires the discovery of uncharted solutions using his solutions as a guide.

How Does One Cut a Triangle? is a work of art, and rarely, perhaps never, does one find the talents of an artist better suited to his intention than we find in Alexander Soifer and this book.       

―Peter D. Johnson, Jr.

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.

―Paul Erdös

It is impossible to convey the spirit of the book by merely listing the problems considered or even a number of solutions. 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.

―L.M. Kelly

Mathematical Reviews

[How Does One Cut a Triangle?] 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.

―Cecil Rousseau

The beginner, who is interested in the book, not only comprehends a situation in a creative mathematical studio, not only is exposed to good mathematical taste, but also acquires elements of modernmathematical culture. And (not less important) the reader imagines the role and place of intuition and analogy in mathematical investigation; he or she fancies the meaning of generalization in modern mathematics and surprising connections between different parts of this science (that are, as one might think, far from each other) that unite them.

―V.G. Boltyanski

SIAM Review

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.

―John Baylis

The Mathematical Gazette