Mathematics Is Beautiful

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.

Mathematical ideas with aesthetic appeal for any mathematically minded person.

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.

Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

Modern life is increasingly relying on digital technology, which in turn runs on mathematics. However, this underlying math is hidden from us. That is mostly a good thing since we do not want to be solving equations and calculating fractions just to get things done in our everyday business. But the mathematical details do matter for anyone who wants to understand how stuff works, or wishes to create something new in the jungle of apps and algorithms. This book takes a look at the mathematical models behind weather forecasting, climate change prediction, artificial intelligence, medical imaging and computer graphics. The reader is expected to have only a curious mind; technical math skills are not needed for enjoying this text.

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.

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."

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.

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.

Imagine that you’ve finally found a parking space after a long and harrowing search, but are now encountering some difficulty in trying to enter this space. Wouldn’t it be great if you knew a formula that allowed you to enter the space without difficulty? Are you annoyed because your soda can doesn’t remain upright during a picnic? Would you like to know why a mirror swaps right and left, but not top and bottom? Are you looking for a mathematical speech to toast your mother-in-law’s 85th birthday? Or do you want to give your heart away mathematically? Dr. Norbert Herrmann provides amusing and entertaining solutions to these and many other problems that we encounter in everyday situations. “A book for teachers, students of mathematics, and anybody who likes unusual and amusing calculations.”