Mathematics And The Aesthetic
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Mathematics And The Aesthetic
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Author : Nathalie Sinclair
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-28
Mathematics And The Aesthetic written by Nathalie Sinclair and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-28 with Mathematics categories.
This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.
Explaining Beauty In Mathematics An Aesthetic Theory Of Mathematics
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Author : Ulianov Montano
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-20
Explaining Beauty In Mathematics An Aesthetic Theory Of Mathematics written by Ulianov Montano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Philosophy categories.
This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics. The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as process theory. The theory comprises explications of three central topics: aesthetic experience (in mathematics), aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities.
Aesthetics Of Interdisciplinarity Art And Mathematics
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Author : Kristóf Fenyvesi
language : en
Publisher: Birkhäuser
Release Date : 2017-11-28
Aesthetics Of Interdisciplinarity Art And Mathematics written by Kristóf Fenyvesi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-28 with Mathematics categories.
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 And Beauty
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Author : Nathalie Sinclair
language : en
Publisher:
Release Date : 2006-09-08
Mathematics And Beauty written by Nathalie Sinclair and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-08 with Education categories.
In this innovative book, Nathalie Sinclair makes a compelling case for the inclusion of the aesthetic in the teaching and learning of mathematics. Using a provocative set of philosophical, psychological, mathematical, technological, and educational insights, she illuminates how the materials and approaches we use in the mathematics classroom can be enriched for the benefit of all learners. While ranging in scope from the young learner to the professional mathematician, there is a particular focus on middle school, where negative feelings toward mathematics frequently begin. Offering specific recommendations to help teachers evoke and nurture their students’ aesthetic abilities, this book: Features powerful episodes from the classroom that show students in the act of developing a sense of mathematical aesthetics. Analyzes how aesthetic sensibilities to qualities such as connectedness, fruitfulness, apparent simplicity, visual appeal, and surprise are fundamental to mathematical inquiry. Includes examples of mathematical inquiry in computer-based learning environments, revealing some of the roles they play in supporting students’ aesthetic inclinations.
Amazing And Aesthetic Aspects Of Analysis
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Author : Paul Loya
language : en
Publisher: Springer
Release Date : 2018-05-11
Amazing And Aesthetic Aspects Of Analysis written by Paul Loya and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.
Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous ε-N and ε-δ definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulæ for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.
Mathematics Of Aesthetics
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Author : Anil Kumar Shukla
language : en
Publisher:
Release Date : 1987
Mathematics Of Aesthetics written by Anil Kumar Shukla and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Aesthetics categories.
The Art Of Mathematics
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Author : Jerry P. King
language : en
Publisher: Springer
Release Date : 2013-11-11
The Art Of Mathematics written by Jerry P. King and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
The beauty of mathematics eludes all but a small, select handful of people. This monumental classic will illuminate the aesthetic delights of mathematics for all to behold. Why should only a tiny aristocracy hold the key to appreciating the elegance of mathematics? Why should intelligent, cultured people, who can easily articulate the brilliance of Shakespeare's imagery, quake at the prospect of deciphering a simple algebraic formula? Jerry King, a mathematics professor and a poet, razes the barriers between a world of two cultures and hands us the tools for appreciating the art and treasures of this elegant discipline. In his fluid, poetic voice, he initiates us into the splendid wonders of the Mathworld. He provides us with an original framework for contemplating mathematics as art. He deepens our ultimate comprehension of art by comparing the beauty of a Rembrandt as well as a Jackson Pollock with the riches to be mined in an elegant proof. Like the great philosophers of the past, Dr. King searches for pure Truth--a quest possible today only in the realm of mathematics. With his infectious enthusiasm, he explains with utmost clarity the intellectually stimulating underpinnings of both pure and applied mathematics. He goes on to decry how our educational system has failed by perfunctorily teaching us mathematics, depriving us of the pillars of beauty upon which mathematics rests. Never before has a book spoken so eloquently to our soul in instilling an appreciation for the grandeur of mathematics. Through Dr. King, the muses of mathematics will no longer sing for others and not for us. The elegant world of mathematics awaits us all to savor.
Beauty In Mathematics Symmetry And Fractality
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Author : Vladimir A. Testov
language : en
Publisher: Infinite Study
Release Date :
Beauty In Mathematics Symmetry And Fractality written by Vladimir A. Testov and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Juvenile Nonfiction categories.
The most important concepts underlying beauty are the concepts of symmetry and fractality, but the relationship of these concepts has not yet remained clear. For centuries, beauty was understood only as a stable order and symmetry. Synergetic worldview allows us to give a new assessment: beauty can be seen as an attractor, the result of self-organization of nature, or the flight of human thought. On the one hand, fractality can be considered one of the manifestations of symmetry in an expansive sense.
Mathematics And Art
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Author : Lynn Gamwell
language : en
Publisher: Princeton University Press
Release Date : 2016
Mathematics And Art written by Lynn Gamwell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Art categories.
This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell's comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians' search for the foundations of their science, such as David Hilbert's conception of mathematics as an arrangement of meaning-free signs, as well as artists' search for the essence of their craft, such as Aleksandr Rodchenko's monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked "What is art?" in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.
Mathematical Aesthetic Principles Nonintegrable Systems
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Author : Murray Muraskin
language : en
Publisher: World Scientific
Release Date : 1995-05-09
Mathematical Aesthetic Principles Nonintegrable Systems written by Murray Muraskin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05-09 with Science categories.
Mathematical aesthetics is not discussed as a separate discipline in other books than this, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as “aesthetic” and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, i.e. the results of integration depend on the integration path. The topic of nonintegrable systems has not been given much attention in other books. Hence we discuss techniques for dealing with such systems.