Mathematics Of Aesthetics
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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.
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.
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 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.
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 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.
Aesthetics
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Author : Joseph Manago
language : en
Publisher: AuthorHouse
Release Date : 2005-04
Aesthetics written by Joseph Manago and has been published by AuthorHouse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04 with Mathematics categories.
Aesthetics: The Beauty of God, Nature, and Art is an anthology of historical, literary, mathematical, musicological, philosophical, political, psychological and scientific papers illuminating the motif of the aesthetic experience and aesthetic value ( beauty ])of God, nature, and art as intrinsic properties of the objects in accord with St. Thomas Aquinas s definition of beauty as that which pleases in the very apprehension of it ] V that is, in the spirit of a moderate realist epistemological view of the objects of the aesthetic experience since, as Aristotle said, Beauty is order, symmetry, and definition. ] The topics are inclusive of the beauty of mathematics as exemplified in hyperbolic non V Euclidean geometry and in the consistency of real analysis and the propositional calculus, the mathematical symmetry of DNA (deoxyribonucleic acid) V the genetic material V and other physical, biological, and artistic objects in terms of the golden ratio ] and the unity of string theory, the Schillinger projective geometrical method of composition of melody in terms of the use of melodic organic forms ] (i.e. the terms of the golden spirals of the Fibonacci summation series) in composing the notes of the melody based upon the principle of expanding intervals, the movie review of Pi (fa) with its focus upon the theme of numerological patterns inherent in all physical and biologic phenomena of the universe (i.e. the ubiquity of the fO, the golden ratio ]) and the theory of its protagonist that diverse systems of nonlinear dynamics share a unifying numerical pattern ( chaos theory ]), the cursive form of hieroglyphics (hieratic) and the mathematical structure of the Rhind Papyrus as illustrative of the beautiful in Egyptian mathematics of the Middle Kingdom, phenomenological and philosophical reflections on the spiritual nature of human self V consciousness (the I ] V soul) which apprehends beauty and expresses aesthetic judgments, the transgender hypothesis ] of the etiology of the neuropsychologic phenomenon of transgenderism and potential stem cell therapy as an aesthetic alternative to the Frankensteinian Benjamin triad, ] the aesthetic disvalue of mental disorder as exemplified in a case analysis of panic disorder, ] American political disorder in terms of the lack of broader FDA and FCC investigatory powers with respect to the marketing of cell phones whose electromagnetic radiofrequency ( RF radiation ]) is associated with biological effects and potential medical hazards, the paralysis of the American government regarding aircraft noise pollution and its serious biological and psychological effects, the inevitability of the American Civil War (1861 V 65) as analyzed in terms of the underlying political and socio V economic disordered relations between North and South (and the implicit moral disorder of slavery and duplicity of Northern and Southern politicians in their support of the war), the un- Constitutional interpretations (and Executive policies thereof) of the Homeland Security Act of 2002 as indicative of a profound political disorder in the American Republic in terms of human and civil rights, the beauty of the musical structure and performance of Rachmaninov s Piano Concerto No. 2 in C Minor (Opus 18) For Piano & Orchestra and Full Moon and Open Arms, the beauty of music, color and the unity of God ( Come Sunday ]) in the life and works of Duke Ellington, a journey to beautiful Mediterranean palaces in The Intruder, the panoply of sights, sounds, and smells ] of Christmas in Brooklyn, the beauty of hearth, gifts, the Church and the Holy Eucharist of Jesus Christ during Christmas in A Christmas Vignette, the beauty of the ministries of the Sisters of Mercy of Brooklyn and the Franciscan Brothers of Brooklyn (and the spiritual beauty of Rev. Mother Catherine McAuley and St. Fran
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.
The Aesthetics Of Science
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Author : Milena Ivanova
language : en
Publisher: Routledge
Release Date : 2020-01-16
The Aesthetics Of Science written by Milena Ivanova and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Philosophy categories.
This volume builds on two recent developments in philosophy on the relationship between art and science: the notion of representation and the role of values in theory choice and the development of scientific theories. Its aim is to address questions regarding scientific creativity and imagination, the status of scientific performances—such as thought experiments and visual aids—and the role of aesthetic considerations in the context of discovery and justification of scientific theories. Several contributions focus on the concept of beauty as employed by practising scientists, the aesthetic factors at play in science and their role in decision making. Other essays address the question of scientific creativity and how aesthetic judgment resolves the problem of theory choice by employing aesthetic criteria and incorporating insights from both objectivism and subjectivism. The volume also features original perspectives on the role of the sublime in science and sheds light on the empirical work studying the experience of the sublime in science and its relation to the experience of understanding. The Aesthetics of Science tackles these topics from a variety of novel and thought-provoking angles. It will be of interest to researchers and advanced students in philosophy of science and aesthetics, as well as other subdisciplines such as epistemology and philosophy of mathematics.