Tessellations

"""Tessellations is an ideal book for precocious students who enjoy mathematics, for teachers, for fans of Escher who are curious about how such patterns are made, for aspiring graphics designers and artists who want to try their hand at creating tessellation patterns, and for working mathematicians looking for an insightful and up-to-date introduction to this vibrant field. The author’s love of the subject and lavish illustrations make the book a joy to explore. Open it to almost any page and there is a dazzling image or figure to draw you in. In short, it is a beautiful book, one that makes a strong case for the printed page, and which invites the reader to engage in the joyfully creative process of producing tessellations."" – The American Mathematical Monthly ""Robert Fathauer’s Tessellations: Mathematics, Art, and Recreation is a gorgeous book. It’s lavishly illustrated with photographs of tessellations and related patterns from nature and architecture; with reproductions of artwork by M. C. Escher and other artists who have found inspiration in tessellations; with the tilings of geometers such as Sir Roger Penrose, Robert Ammann, and Casey Mann; and, most of all, with the author’s own creations. The reader will need an interest in mathematics, but no great background; the level of rigor is only a little higher than what aficionados of the late Martin Gardner will remember. To take advantage of this, the book is liberally sprinkled with activities aimed at the K-12 classroom, including handouts, lists of vocabulary words, and (where relevant) CCSSM standards. [. . .] The range of topics is wide, and each one is explored fairly deeply, with its relevant history. [. . .] Finally, Fathauer is not just a mathematician but also an artist. He shares his artistic tips freely here, including, in Chapter 13-19, some really good instructions on how to create an Escher-style tiling based on various symmetries. If you are a high school math teacher and you bring a copy of this book in to work, you may need to hide it from the art teacher!"" – CMS Notes ""A treasure trove of geometric delights, this book will draw you into the beautiful and deep questions of mathematics that come from the simple question of how shapes fit together."" – Edmund Harriss, University of Arkansas and the co-author of Patterns of the Universe: A Coloring Adventure in Math and Beauty ""A beautifully presented, comprehensive introduction to tessellations––what tessellation enthusiasts and teachers (at all levels) have wished for. The author, a talented tessellations artist himself, captures the fascination of tessellations through beautiful color illustrations. His chapters touch on every aspect of tessellations—their history, the many different types, where they occur, their symmetries, ways in which they are classified, their practical uses. More than half of the book is devoted to thoughtful advice and careful descriptions of how to create various kinds of tessellations. Questions and activities (often with helpful worksheets or templates) throughout are useful not only for teachers and students, but for anyone who wishes to test their understanding. This is truly an indispensible book for all those who want to learn about, teach, or make tessellations."" – Doris Schattschneider, Recipient of Mathematical Association of America's Carl B. Allendoerfer Award and the author of M.C. Escher Kaleidocycles ""Fathauer's book is a fun, accessible, and lavishly illustrated guide to the universe of tessellations. You can study the structure of tessellations, and even learn to make your own. It's certain to appeal to anyone who wants to explore this beautiful topic at the intersection of art and mathematics."" – Craig Kaplan, University of Waterloo ""A gorgeously illustrated romp through tiling theory, a pleasure to read and fun for all ages and levels and a must for every geometry classroom and geometry buff’s bookshelf! – Chaim Goodman-Strauss, University of Arkansas and the co-author of The Symmetries of Things"