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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 modern mathematical 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.

Combinatorial geometry. --- Electronic books. -- local. --- Triangle. --- Combinatorial geometry --- Triangle --- Geometry --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Circles of the triangle --- Geometric combinatorics --- Geometrical combinatorics --- Mathematics. --- Algebra. --- Geometry. --- Combinatorics. --- Mathematics, general. --- Geometry, Plane --- Combinatorial analysis --- Discrete geometry --- Math --- Science --- Combinatorics --- Mathematical analysis --- Euclid's Elements

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I have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel… I found it hard to stop reading before I finished (in two days) the whole text. Soifer engages the reader's attention not only mathematically, but emotionally and esthetically. May you enjoy the book as much as I did! –Branko Grünbaum University of Washington You are doing great service to the community by taking care of the past, so the things are better understood in the future. –Stanislaw P. Radziszowski, Rochester Institute of Technology They [Van der Waerden’s sections] meet the highest standards of historical scholarship. –Charles C. Gillispie, Princeton University You have dug up a great deal of information – my compliments! –Dirk van Dalen, Utrecht University I have just finished reading your (second) article "in search of van der Waerden". It is a masterpiece, I could not stop reading it... Congratulations! –Janos Pach, Courant Institute of Mathematics "Mathematical Coloring Book" will (we can hope) have a great and salutary influence on all writing on mathematics in the future.“ –Peter D. Johnson Jr., Auburn University Just now a postman came to the door with a copy of the masterpiece of the century. I thank you and the mathematics community should thank you for years to come. You have set a standard for writing about mathematics and mathematicians that will be hard to match. –Harold W. Kuhn, Princeton University The beautiful and unique Mathematical coloring book of Alexander Soifer is another case of ``good mathematics''… and presenting mathematics as both a science and an art… It is difficult to explain how much beautiful and good mathematics is included and how much wisdom about life is given. –Peter Mihók, Mathematical Reviews.

Ramsey theory. --- Ramsey theory --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematics. --- History. --- Mathematical logic. --- Combinatorics. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Combinatorial analysis --- Graph theory --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Combinatorics --- Mathematical analysis --- Annals --- Auxiliary sciences of history --- Math --- Science

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Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year. This book presents a year-by-year history of the CMO from 2004–2013 with all the problems from the competitions and their solutions. Additionally, the book includes 10 further explorations, bridges from solved Olympiad problems to ‘real’ mathematics, bringing young readers to the forefront of various fields of mathematics. This book contains more than just problems, solutions, and event statistics — it tells a compelling story involving the lives of those who have been part of the Olympiad, their reminiscences of the past and successes of the present. I am almost speechless facing the ingenuity and inventiveness demonstrated in the problems proposed in the third decade of these Olympics. However, equally impressive is the drive and persistence of the originator and living soul of them. It is hard for me to imagine the enthusiasm and commitment needed to work singlehandedly on such an endeavor over several decades. —Branko Grünbaum, University of Washington After decades of hunting for Olympiad problems, and struggling to create Olympiad problems, he has become an extraordinary connoisseur and creator of Olympiad problems.  The Olympiad problems were very good, from the beginning, but in the third decade the problems have become extraordinarily good.  Every brace of 5 problems is a work of art.  The harder individual problems range in quality from brilliant to work-of-genius… The same goes for the “Further Explorations” part of the book.  Great mathematics and mathematical questions are immersed in a sauce of fascinating anecdote and reminiscence.  If you could have only one book to enjoy while stranded on a desert island, this would be a good choice.   —Peter D. Johnson, Jr., Auburn University Like Gauss, Alexander Soifer would not hesitate to inject Eureka! at the right moment. Like van der Waerden, he can transform a dispassionate exercise in logic into a compelling account of sudden insights and ultimate triumph. — Cecil Rousseau Chair, USA Mathematical Olympiad Committee A delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved. —Paul Erdős The book is a gold mine of brilliant reasoning with special emphasis on the power and beauty of coloring proofs. Strongly recommended to both serious and recreational mathematicians on all levels of expertise. —Martin Gardner.

Mathematics. --- Algebra. --- Geometry. --- Mathematical logic. --- Number theory. --- Number Theory. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical. --- Number study --- Numbers, Theory of --- Algebra --- Mathematics --- Euclid's Elements --- Mathematical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Competitions --- Soifer Mathematical Olympiad.

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Retelling the best solutions and sharing the secrets of discovery are part of the process of teaching problem solving. Ideally, this process is characterized by mathematical skill, good taste, and wit. It is a characteristically personal process and the best such teachers have surely left their personal marks on students and readers. Alexander Soifer is a teacher of problem solving and his book, Mathematics as Problem Solving, is designed to introduce problem solving to the next generation. --Cecil Rousseau The American Mathematical Monthly The problems faithfully reflect the world famous Russian school of mathematics, whose folklore is carefully interwoven with more traditional topics. Many of the problems are drawn from the author's rich repertoire of personal experiences, dating back to his younger days as an outstanding competitor in his native Russia, and spanning decades and continents as an organizer of competitions at the highest level. --George Bersenyi The book contains a very nice collection of problems of various difficulty. I particularly liked the problems on combinatorics and geometry. --Paul Erdos Professor Soifer has put together a splendid collection of elementary problems designed to lead students into significant mathematical concepts and techniques. Highly recommended. --Martin Gardner To assemble so much material of the type used in Mathematical Olympiads, which has been tried and tested there, is unusual. To then present it in a form which develops themes, supported by relevant examples and problems for the reader, does the author great credit. --R. W. Whitworth The Mathematical Gazette.

Geometry --- geometrie --- algebra --- wiskunde --- Mathematics --- Discrete mathematics --- discrete wiskunde --- Algebra --- Problem solving. --- Algebra. --- Combinatorics. --- Geometry. --- Mathematics. --- Mathematics, general. --- Math --- Science --- Euclid's Elements --- Combinatorics --- Mathematical analysis

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Mathematical logic --- Discrete mathematics --- Mathematics --- discrete wiskunde --- geschiedenis --- wiskunde --- logica