A fascinating exploration of the pentagon and its role in various cultures The pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon’s wide-ranging history, no single book has explored the important role of this shape in various cultures, until now. Richly illustrated, Pentagons and Pentagrams offers a sweeping view of the five-sided polygon, revealing its intriguing geometric properties and its essential influence on a variety of fields. Traversing time, Eli Maor narrates vivid stories, both celebrated and unknown, about the pentagon and pentagram. He discusses the early Pythagoreans, who ascribed to the pentagon mythical attributes, adopted it as their emblem, and figured out its construction with a straightedge and compass. Maor looks at how a San Diego housewife uncovered four previously unknown types of pentagonal tilings, and how in 1982 a scientist’s discovery of fivefold symmetries in certain alloys caused an uproar in crystallography and led to a Nobel Prize. Maor also discusses the pentagon’s impact on many buildings, from medieval fortresses to the Pentagon in Washington, D.C. Eugen Jost’s superb illustrations provide sumptuous visual context, and the book’s puzzles and mazes offer fun challenges for readers, with solutions given in an appendix.

An exquisite visual celebration of the 2,500-year history of geometry If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

'Everyone interested in geometric dissections, and this kind of puzzles, either mathematically or recreationally will embrace this publication. But also the readers interested in the history and certainly those who became curious about this mystery man and his manuscript, after reading Frederickson’s 2006 book, will be fully satisfied with this respectful reproduction eventually made available for a general public.'European Mathematical Society'Ernest Irving Freese's Geometric Transformations does not just uncover a mathematical gem. It is also a piece of art and a mind-puzzling set of ingenious dissections done by a master of architectural drawings and amateur mathematician. It is a practical book that shows the beauty of dissection and how we can get from a polygon to another by cutting it to pieces and recollect them in some special way. The book is written in a very elegant style, and nicely presented. Freese’s manuscript was photographed and wasn’t altered in any way — this preserved its beauty. Freese’s drawing shows ingenuity and it shows how meticulous he was. For those people who are interested in geometry or in geometric dissections and for those who admire puzzles and recreational mathematics this book is a must.' (See Full Review)MAA ReviewsA geometric dissection is a cutting of a geometric figure (such as a regular polygon, or a star, or a cross) into pieces that we can rearrange to form another geometric figure. The best dissections are beautiful and possess economy (few pieces), symmetry, or hingeability. They are often challenging to discover.Ernest Irving Freese was an architect who lived and worked in Los Angeles until his death in 1957. Shortly before he passed away, he completed a 200-page manuscript on geometric dissection, the first book-length treatment on that subject. Freese included elegant drawings of dissections that were both original and clever. After his death the manuscript lay forgotten in his former house until Greg Frederickson set in motion its recovery in 2003. What a treat that it was rescued!Frederickson's book sketches a history of geometric dissections and a biography of Freese, followed by a refurbished copy of Freese's manuscript interleaved with a commentary that highlights Freese's major contributions as well as singular improvements made by Frederickson and others after Freese.This book introduces Freese and his creations to math puzzle enthusiasts, by way of his engaging manuscript, his wild adventures, and his lovely dissections. Frederickson also includes remarkable designs that improve on Freese's work, and packs this book with nifty illustrations and tidbits that may well leave you speechless!

These novel and original dissections will be a gold mine for math puzzle enthusiasts and for math educators.

This book provides an interdisciplinary guide to quasicrystals, the 2011 Nobel Prize in Chemistry winning topic, by presenting an up-to-date and detailed introduction to the many fundamental aspects and applications of quasicrystals science. It reviews the most characteristic features of the peculiar geometric order underlying their structure and their reported intrinsic physical properties, along with their potential for specific applications. The role of quasiperiodic order in science and technology is also examined by focusing on the new design capabilities provided by this novel ordering of matter. This book is specifically devoted to promoting the very notion of quasiperiodic order, and to spur its physical implications and technological capabilities. It, therefore, explores the fundamental aspects of intermetallic, photonic, and phononic quasicrystals, as well as soft-matter quasicrystals, including their intrinsic physical and structural properties. In addition, it thoroughly discusses experimental data and related theoretical approaches to explain them, extending the standard treatment given in most current solid state physics literature. It also explores exciting applications in new technological devices of quasiperiodically ordered systems, including multilayered quasiperiodic systems, along with 2D and 3D designs, whilst outlining new frontiers in quasicrystals research. This book can be used as a reader-friendly introductory text for graduate students, in addition to senior scientists and researchers coming from the fields of physics, chemistry, materials science, and engineering. Key features: • Provides an updated and detailed introduction to the interdisciplinary field of quasicrystals in a tutorial style, considering both fundamental aspects and additional freedom degrees provided by designs based on quasiperiodically ordered materials. • Includes 50 fully worked out exercises with detailed solutions, motivating, and illustrating the different concepts and notions to provide readers with further learning opportunities. • Presents a complete compendium of the current state of the art knowledge of quasicrystalline matter, and outlines future next generation materials based on quasiperiodically ordered designs for their potential use in useful technological devices. Dr. Enrique Maciá-Barber is Professor of condensed matter physics at the Universidad Complutense de Madrid. His research interests include the thermoelectric properties of quasicrystals and DNA biophysics. In 2010 he received the RSEF- BBVA Foundation Excellence Physics Teaching Award. His book Aperiodic Structures in Condensed Matter: Fundamentals and Applications (CRC Press, Boca-Raton, 2009) is one of the Top Selling Physics Books according to YBP Library Services.

In Patterns: Design and Composition, M. A. Hann and I. S. Moxon present guidelines for the original design and composition of regular patterns alongside an understanding of the inherent structures of these patterns. Starting with the compositional elements, Hann and Moxon take the reader through patterns in the environment, early forms of patterns and aspects of classification based on circles, squares, triangles and symmetry. With 250 images sourced from past examples as well as student work, this essential read for design students and researchers demonstrates how simplicity begets complexity in the design and composition of regular patterns.

What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.

One of the Top Selling Physics Books according to YBP Library ServicesOrder can be found in all the structures unfolding around us at different scales, including in the arrangements of matter and in energy flow patterns. Aperiodic Structures in Condensed Matter: Fundamentals and Applications focuses on a special kind of order referred to as aperiod

Since about 1985, crop circles have become a more well-known phenomenon. In the meantime, about 10,000 crop circles have appeared in more than 50 countries. However, well over half of them come from southern England in the area of Stonehenge, Woodhenge, Silbury Hill, White Horse and other prehistoric monuments. Some of them can be proved to have been made by humans, but others just as certainly have not been made by humans - this is not the starting situation one would wish for as a researcher ... In the present book 300 of these crop circles are examined more closely. It turns out that they contain approx. 100 elements which appear in many crop circles. Their geometrical form has an easily recognizable meaning. Therefore, with the help of these "words", the crop circles composed of them can be read like "sentences". The meaning is almost always the same: a representation of how individuality unfolds. Therefore, there are many similarities with astrology or the chakra system, for example. This analytical approach is complemented by 50 dream journeys into individual crop circles, which makes the picture that arises from the analytical observation of the crop circles even more rounded. Thereby a first impression can be gained of the language of the collective subconsciousness - which words and which grammar it uses: It is a "music of geometry".

This is a book of mathematical stories — funny and puzzling mathematical stories. They tell of villains who try to steal secrets, heroes who encode their messages, and mathematicians who spend years on end searching for the best way to pile oranges. There are also stories about highway confusions occurring when the rules of Cartesian geometry are ignored, small-change errors due to ignorance of ancient paradoxes, and mistakes in calendars arising from poor numerical approximations. This book is about the power and beauty of mathematics. It shows mathematics in action, explained in a way that everybody can understand. It is a book for enticing youngsters and inspiring teachers. Nuno Crato is a leading science writer and mathematician, whose entertaining essays have won a number of international awards.