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This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.

Mathematics. --- Mathematics in Art and Architecture. --- Mathematics in art. --- Math --- Science

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“The book is an original, interesting and opportune contribution to an area not contemplated in geometry courses.” (Mathematical Reviews Clippings) “Angelo Mazzotti’s All Sides to an Oval is a fundamental book for anyone working with oval forms from the point of view of the geometric control of the shapes.” (Nexus Netw J) “We think that the reader, whatever his or her academic background, will enjoy the logical sequence of the reasoning, the drawings, and the clarity of language in this book.” (The Mathematical Intelligencer) This is the second edition of the only book dedicated to the Geometry of Polycentric Ovals. It includes problem solving constructions and mathematical formulas. For anyone interested in drawing or recognizing an oval, this book gives all the necessary construction, representation and calculation tools. More than 30 basic construction problems are solved, with references to Geogebra animation videos, plus the solution to the Frame Problem and solutions to the Stadium Problem. A chapter (co-written with Margherita Caputo) is dedicated to totally new hypotheses on the project of Borromini’s oval dome of the church of San Carlo alle Quattro Fontane in Rome. Another one presents the case study of the Colosseum as an example of ovals with eight centres as well as the case study of Perronet’s Neuilly bridge, a half oval with eleven centres. The primary audience is: architects, graphic designers, industrial designers, architecture historians, civil engineers; moreover, the systematic way in which the book is organised could make it a companion to a textbook on descriptive geometry or on CAD. Added features in the 2nd edition include: the revised hypothesis on Borromini’s project for the dome of the church of San Carlo alle Quattro Fontane in Rome, an insight into the problem of finding a single equation to represent a four-centre oval, a suggestion for a representation of a four-centre oval using Geogebra, formulas for parameters of ovals with more than 4 centres and the case study of the eleven-centre half-oval arch used to build the XVIII century Neuilly bridge in Paris.

Geometry. --- Mathematics. --- Mathematics in Art and Architecture. --- Math --- Science --- Mathematics --- Euclid's Elements

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This book is written in a style that uncovers the mathematical theories hidden in our daily lives, using examples of patterns that appear in nature, arts, traditional crafts, as well as mathematical mechanics in architectural techniques. The authors believe that through conversations between students and mathematicians, readers may learn about the methods used by the originators of these theories―their trials, errors, and triumphs―in reaching their various conclusions. The goal is to help readers refine their mathematical sense in terms of formulating valuable questions and pursuing them. In addition, the book aims to provide enjoyment in the application of mathematical principles to beautiful art and design by using examples that highlight the wonders and mysteries of these works found in our daily lives. To achieve these goals, the book tackles the latest exquisite results on polygons and polyhedra and the dynamic history of geometric research found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth and refers to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book enables readers to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity. In this second edition, many new results, and elegant proofs on a variety of topics have been added, enhancing the book’s rich content even further.

Mathematics. --- Arts. --- Architecture --- Polytopes. --- Discrete mathematics. --- Mathematics in Art and Architecture. --- Discrete Mathematics.

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The goal of this Handbook is to become an authoritative source with chapters that show the origins, unification, and points of similarity between different disciplines and mathematics. Some chapters will also show bifurcations and the development of disciplines which grow to take on a life of their own. Science and Art are used as umbrella terms to encompass the physical, natural and geological sciences, as well as the visual and performing arts. As arts imagine possibilities, science attempts to generate models to test possibilities, mathematics serves as the tool. This handbook is an indispensable collection to understand todays effort to build bridges between disciplines. It answers questions such as: What are the origins of interdisciplinarity in mathematics? What are cross-cultural components of interdisciplinarity linked to mathematics? What are contemporary interdisciplinary trends? Section Editors: Michael J. Ostwald, University of Newcastle (Australia) Kyeong-Hwa Lee, Seoul National University (South Korea) Torsten Lindström, Linnaeus University (Sweden) Gizem Karaali, Pomona College (USA) Ken Valente, Colgate University, (USA) Consulting Editors: Alexandre Borovik, Manchester University (UK) Daina Taimina, Independent Scholar, Cornell University (USA) Nathalie Sinclair, Simon Fraser University (Canada).

Mathematics. --- Social sciences. --- Mathematics in Art and Architecture. --- Mathematics in Music. --- Mathematics in the Humanities and Social Sciences.

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With the poems written by winner of the Posner Poetry Award from the Council of Wisconsin Writers in 2005, this coffee-table book will delight and inform general readers curious about ideas of chaos, fractals, and nonlinear complex systems. Developed out of ten years of interdisciplinary seminars in chaos and complex systems at the University of Wisconsin-Madison, it features multiple ways of knowing: Robin Chapman's poems of everyday experience of change in a complex world, associated metaphorically with Julien Clinton Sprott's full-color computer art generated from billions of versions of on

Dynamics. --- Chaotic behavior in systems. --- Fractals. --- Nonlinear theories. --- Mathematics in art. --- Mathematics in literature. --- Digital art. --- Computer art.