Geometric Etudes in Combinatorial Mathematics ORIGINAL ETUDES Tiling a Checker Rectangle Proofs of Existence A Word About Graphs Ideas of Combinatorial Geometry NEW LANDSCAPE OR THE VIEW 18 YEARS LATER Mitya Karabash and a Tiling Conjecture Norton Starr’s 3 Dimensional Tromino Tiling Large Progress in Small Ramsey Numbers The Borsuk Problem Conquered Etude on the Chromatic Number of the Plane. 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. —Don Chakerian THE AMERICAN MATHEMATICAL MONTHLY Alexander Soifer’s Geometrical Etudes in Combinatorial Mathematics is concerned with beautiful mathematics and it will likely occupy a special and permanent place in the mathematical literature challenging and inspiring both novice and expert readers with surprising and exquisite problems and theorems… He conveys the joy of discovery as well as anyone and he has chosen a topic that will stand the test of time. —Cecil Rousseau MEMPHIS STATE UNIVERSITY Each time I looked at Geometrical Etudes in Combinatorial Mathematics I found something that was new and surprising to me even after more than fifty years working in combinatorial geometry. The new edition has been expanded (and updated where needed) by several new delightful chapters. The careful and gradual introduction of topics and results is equally inviting for beginners and for jaded specialists. I hope that the appeal of the book will attract many young mathematicians to the visually attractive problems that keep you guessing how the questions will be answered in the end. —Branko Grünbaum UNIVERSITY OF WASHINGTON SEATTLE All of Alexander Soifer’s books can be viewed as excellent and artful entrees to mathematics in the MAPS mode... Different people will have different preferences among them but here is something that Geometric Etudes does better than the others: after bringing the reader into a topic by posing interesting problems starting from a completely elementary level it then goes deep. The depth achieved is most spectacular in Chapter 4 on Combinatorial Geometry which could be used as part or all of a graduate course on the subject but it is also pretty impressive in Chapter 3 on graph theory and in Chapter 2 where the infinite pigeon hole principle (infinitely many pigeons finitely many holes) is used to prove theorems in an important subset of the set of fundamental theorems of analysis. —Peter D. Johnson Jr. AUBURN UNIVERSITY This interesting and delightful book … 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. —Paul Erdos.