Geometric Etudes in Combinatorial Mathematics

From the book reviews: "This book itself has also a good chance to occupy a permanent place in the mathematical literature. Among its virtues is the lively and fluent style, in which it introduces and explains the problems. ... In summing up, we warmly recommend this book to any interested reader: take and read, and dip into the exercises and the problems ... ." (Gabor Gevay, Acta Scientiarum Mathematicarum (Szeged), Vol. 77 (3-4), 2011) Characteristically, each of the topics included in the book require very little in the way of preparation and evolve fast into open questions and research level conjectures...This is a delightful book that will be welcomed enthusiastically by students and organizers of mathematical circles and mathematics fans.---Alexander Bogomolny 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 thoese 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. ---The American Mathematical Monthly

• 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.