Mathematics And Beauty

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Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

Ulianov Montano
Explaining Beauty in Mathematics An Aesthetic Theory of Mathematics Book PDF

Author : Ulianov Montano
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 51,8 Mb
Release : 2013-12-20
Category : Philosophy
ISBN : 9783319034522

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Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics by Ulianov Montano Pdf

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.

The Divine Proportion

H. E. Huntley
The Divine Proportion Book PDF

Author : H. E. Huntley
Publisher : Courier Corporation
Page : 208 pages
File Size : 54,7 Mb
Release : 2012-06-08
Category : Mathematics
ISBN : 9780486131870

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The Divine Proportion by H. E. Huntley Pdf

Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.

The Beauty of Doing Mathematics

Serge Lang
The Beauty of Doing Mathematics Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 42,5 Mb
Release : 1985-09-04
Category : Mathematics
ISBN : 0387961496

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The Beauty of Doing Mathematics by Serge Lang Pdf

If someone told you that mathematics is quite beautiful, you might be surprised. But you should know that some people do mathematics all their lives, and create mathematics, just as a composer creates music. Usually, every time a mathematician solves a problem, this gives rise to many oth ers, new and just as beautiful as the one which was solved. Of course, often these problems are quite difficult, and as in other disciplines can be understood only by those who have studied the subject with some depth, and know the subject well. In 1981, Jean Brette, who is responsible for the Mathematics Section of the Palais de la Decouverte (Science Museum) in Paris, invited me to give a conference at the Palais. I had never given such a conference before, to a non-mathematical public. Here was a challenge: could I communicate to such a Saturday afternoon audience what it means to do mathematics, and why one does mathematics? By "mathematics" I mean pure mathematics. This doesn't mean that pure math is better than other types of math, but I and a number of others do pure mathematics, and it's about them that I am now concerned. Math has a bad reputation, stemming from the most elementary levels. The word is in fact used in many different contexts. First, I had to explain briefly these possible contexts, and the one with which I wanted to deal.

Mathematics and Beauty

Nathalie Sinclair
Mathematics and Beauty Book PDF

Author : Nathalie Sinclair
Publisher : Unknown
Page : 212 pages
File Size : 46,9 Mb
Release : 2006-09-08
Category : Education
ISBN : STANFORD:36105114444016

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Mathematics and Beauty by Nathalie Sinclair Pdf

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.

Math Art

Stephen Ornes
Math Art Book PDF

Author : Stephen Ornes
Publisher : Sterling New York
Page : 0 pages
File Size : 43,9 Mb
Release : 2019
Category : MATHEMATICS
ISBN : 1454930446

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Math Art by Stephen Ornes Pdf

The worlds of visual art and mathematics beautifully unite in this spectacular volume by award-winning writer Stephen Ornes. He explores the growing sensation of math art, presenting such pieces as a colorful crocheted representation of non-Euclidian geometry that looks like sea coral and a 65-ton, 28-foot-tall bronze sculpture covered in a space-filling curve. We learn the artist's story for every work, plus the mathematical concepts and equations behind the art.

Beautiful Mathematics

Martin Erickson
Beautiful Mathematics Book PDF

Author : Martin Erickson
Publisher : MAA
Page : 193 pages
File Size : 50,9 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9780883855768

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Beautiful Mathematics by Martin Erickson Pdf

Mathematical ideas with aesthetic appeal for any mathematically minded person.

The Golden Ratio

Gary B. Meisner
The Golden Ratio Book PDF

Author : Gary B. Meisner
Publisher : Quarto Publishing Group USA
Page : 227 pages
File Size : 46,5 Mb
Release : 2018-10-23
Category : Mathematics
ISBN : 9780760360262

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The Golden Ratio by Gary B. Meisner Pdf

This enlightening and gorgeously illustrated book explores the beauty and mystery of the divine proportion in art, architecture, nature, and beyond. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. Author Gary Meisner has spent decades researching the subject, investigating and collaborating with people across the globe in dozens of professions and walks of life. In The Golden Ratio, he shares his enlightening journey. Exploring the long history of this fascinating number, as well as new insights into its power and potential applications, The Golden Ratio invites you to take a new look at this timeless topic.

Mathematics and Art

Lynn Gamwell
Mathematics and Art Book PDF

Author : Lynn Gamwell
Publisher : Princeton University Press
Page : 576 pages
File Size : 49,6 Mb
Release : 2016
Category : Art
ISBN : 9780691165288

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Mathematics and Art by Lynn Gamwell Pdf

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.

Mathematics is Beautiful

Heinz Klaus Strick
Mathematics is Beautiful Book PDF

Author : Heinz Klaus Strick
Publisher : Springer Nature
Page : 370 pages
File Size : 54,9 Mb
Release : 2021-06-24
Category : Mathematics
ISBN : 9783662626894

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Mathematics is Beautiful by Heinz Klaus Strick Pdf

In 17 chapters, this book attempts to deal with well-known and less well-known topics in mathematics. This is done in a vivid way and therefore the book contains a wealth of colour illustrations. It deals with stars and polygons, rectangles and circles, straight and curved lines, natural numbers, square numbers and much more. If you look at the illustrations, you will discover plenty of exciting and beautiful things in mathematics. The book offers a variety of suggestions to think about what is depicted and to experiment in order to make and check your own assumptions. For many topics, no (or only few) prerequisites from school lessons are needed. It is an important concern of the book that young people find their way to mathematics and that readers whose school days are some time ago discover new things. The numerous references to internet sites and further literature help in this respect. "Solutions" to the suggestions interspersed in the individual sections can be downloaded from the Springer website. The book was thus written for everyone who enjoys mathematics or who would like to understand why the book bears this title. It is also aimed at teachers who want to give their students additional or new motivation to learn. This book is a translation of the original German 2nd edition Mathematik ist schön by Heinz Klaus Strick, published by Springer-Verlag GmbH, DE, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). In the subsequent editing, the author, with the friendly support of John O'Connor, St Andrews University, Scotland, tried to make it closer to a conventional translation. Still, the book may read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

Beautiful Symmetry

Alex Berke
Beautiful Symmetry Book PDF

Author : Alex Berke
Publisher : MIT Press
Page : 165 pages
File Size : 41,7 Mb
Release : 2020-02-18
Category : Mathematics
ISBN : 9780262538923

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Beautiful Symmetry by Alex Berke Pdf

A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.

Lost in Math

Sabine Hossenfelder
Lost in Math Book PDF

Author : Sabine Hossenfelder
Publisher : Basic Books
Page : 277 pages
File Size : 46,7 Mb
Release : 2018-06-12
Category : Science
ISBN : 9780465094264

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Lost in Math by Sabine Hossenfelder Pdf

In this "provocative" book (New York Times), a contrarian physicist argues that her field's modern obsession with beauty has given us wonderful math but bad science. Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

The Seduction of Curves

Allan McRobie
The Seduction of Curves Book PDF

Author : Allan McRobie
Publisher : Princeton University Press
Page : 168 pages
File Size : 49,8 Mb
Release : 2017-09-19
Category : Art
ISBN : 9780691175331

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The Seduction of Curves by Allan McRobie Pdf

In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world--from our bodies to Salvador Dalí's paintings and the space-time fabric of the universe itself. The book focuses on seven curves--the fold, cusp, swallowtail, and butterfly, plus the hyperbolic, elliptical, and parabolic "umbilics"--and describes the surprising origins of their taxonomy in the catastrophe theory of mathematician René Thom.

The Beauty of Mathematics in Computer Science

Jun Wu
The Beauty of Mathematics in Computer Science Book PDF

Author : Jun Wu
Publisher : CRC Press
Page : 288 pages
File Size : 41,9 Mb
Release : 2018-11-20
Category : Business & Economics
ISBN : 9781351689113

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The Beauty of Mathematics in Computer Science by Jun Wu Pdf

The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were surprised to find that many daily-used IT technologies were so tightly tied to mathematical principles. For example, the automatic classification of news articles uses the cosine law taught in high school. The book covers many topics related to computer applications and applied mathematics including: Natural language processing Speech recognition and machine translation Statistical language modeling Quantitive measurement of information Graph theory and web crawler Pagerank for web search Matrix operation and document classification Mathematical background of big data Neural networks and Google’s deep learning Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese Internet users from 2006-2010. The blogs had more than 2 million followers. Wu received PhD in computer science from Johns Hopkins University and has been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded 19 US patents during his 10-year tenure there. Wu became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.

Mathematics, Poetry, and Beauty

Ron Aharoni
Mathematics Poetry and Beauty Book PDF

Author : Ron Aharoni
Publisher : World Scientific Publishing Company
Page : 0 pages
File Size : 42,5 Mb
Release : 2015
Category : Literature and science
ISBN : 9814602949

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Mathematics, Poetry, and Beauty by Ron Aharoni Pdf

What does mathematics have to do with poetry? Seemingly, nothing. Mathematics deals with abstractions while poetry with emotions. And yet, the two share something essential: Beauty. "Euclid alone has looked on beauty bare," says the title of a poem by Edna St. Vincent Millay.A winner of the CHOICE Outstanding Academic Title 2015, "Mathematics, Poetry and Beauty" tries to solve the secret of the similarity between the two domains. It tries to explain how a mathematical argument and a poem can move us in the same way. Mathematical and poetic techniques are compared, with the aim of showing how they evoke the same sense of beauty.The reader may find that, as Bertrand Russell said, "Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty hold and austere, like that of sculpture ... sublimely pure, and capable of a stern perfection such as only the greatest art can show."

Beauty in Mathematics: Symmetry and Fractality

Vladimir A. Testov
Beauty in Mathematics Symmetry and Fractality Book PDF

Author : Vladimir A. Testov
Publisher : Infinite Study
Page : 13 pages
File Size : 49,9 Mb
Release : 2024-06-28
Category : Juvenile Nonfiction
ISBN : 8210379456XXX

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Beauty in Mathematics: Symmetry and Fractality by Vladimir A. Testov Pdf

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.