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.

The purpose of this book is to analyze the interdisciplinary aspects of mathematics and geometry in reference to nature, art, and architecture.In Chapter 1, we introduce symmetry and its different meanings. Symmetry is a notion, which has been applied in the arts and architecture to find harmony and beauty. It joins aesthetics and practice, science and economy, mathematics and philosophy. In this chapter, we also analyze the influence of Vitruvius and the concept of old symmetry, received by the Renaissance. It is also interesting to note how in contemporary architecture there is often the presence of the "break" of symmetry (for example in the Frank O. Gehry's works).Chapter 2 explains how proportions, and in particular, the golden section, has introduced aesthetic canons that have strongly influenced many artists like Polycletus, and architects, from Ictinus to Le Corbusier.In Chapter 3, we discover how curves and spirals find their application in artistic works, for example in Mycenaean jewelry, and architectural works, from the Baroque of Francesco Borromini to the Land Art of Smithson.Chapter 4 presents the importance and influence that Platonic solids and polyhedrons have had on philosophy and art through different historical periods and different cultures. For instance, we look at how Platonic solids are connected to the theory of Empedocles' elements and Hippocrates' theory of humors.Chapter 5 describes surfaces, discovering how different cultures have used them in different manners, including Roman aqueducts, iron bridges, and finally arriving on modern structures that base their forms on hyperboloids and paraboloids.In Chapter 6, we introduce fractal geometry, as a geometry that tries to explain nature's irregular shapes, trying to overcome the limitations imposed by "old" Euclidean geometry. We also analyze how fractal geometry has influenced architecture in this century.

The Routledge Companion to Interdisciplinary Studies in Singing, Volume II: Education examines the many methods and motivations for vocal pedagogy, promoting singing not just as an art form arising from the musical instrument found within every individual but also as a means of communication with social, psychological, and didactic functions. Presenting research from myriad fields of study beyond music—including psychology, education, sociology, computer science, linguistics, physiology, and neuroscience—the contributors address singing in three parts: Learning to Sing Naturally Formal Teaching of Singing Using Singing to Teach In 2009, the Social Sciences and Humanities Research Council of Canada funded a seven-year major collaborative research initiative known as Advancing Interdisciplinary Research in Singing (AIRS). Together, global researchers from a broad range of disciplines addressed three challenging questions: How does singing develop in every human being? How should singing be taught and used to teach? How does singing impact wellbeing? Across three volumes, The Routledge Companion to Interdisciplinary Studies in Singing consolidates the findings of each of these three questions, defining the current state of theory and research in the field. Volume II: Education focuses on the second question and offers an invaluable resource for anyone who identifies as a singer, wishes to become a singer, works with singers, or is interested in the application of singing for the purposes of education.

This book celebrates the 15th anniversary of the bi-annual symposium series Mathematics and its Connections to the Arts and Sciences (MACAS), which was first held in 2005 following the continued collaboration of an international group of researchers from ICME Topic Study Group 21. The MACAS-conferences bring together scientists and educators who are interested in the connection between mathematics, arts and science in educational curriculum, while emphasizing on, as well as researching about, the role of mathematics. By pooling together these different approaches and viewpoints between mathematics, arts and sciences, this book reveals possible synergies and paths for collaborations. In view of the challenges of the 21st century, a modern approach to education with a focus on multi- and interdisciplinarity is more important than ever. The role of mathematics assumes a key role in this approach as it is connected to all other disciplines, such as STEM education, physics, chemistry, biology, aesthetics and language, and can serve as a bridge between them. This book discusses, amongst others, the curricular approaches to integrate mathematics and other disciplines, the importance of mathematical modelling and the interdisciplinarity ways for learning and studying of mathematics, as well as the intercultural dimensions of mathematics and mathematics in the digital era. All topics will be presented from very different perspectives and regarding very different contexts, including digitization, culture and sustainability. This unique collection will serve as a very valuable and compact source for all above mentioned scientists and educators, as well as for use in advanced teacher education courses.

As interactive application software such as apps, installations, and multimedia presentations have become pervasive in everyday life, more and more computer scientists, engineers, and technology experts acknowledge the influence that exists beyond visual explanations. Computational Solutions for Knowledge, Art, and Entertainment: Information Exchange Beyond Text focuses on the methods of depicting knowledge-based concepts in order to assert power beyond a visual explanation of scientific and computational notions. This book combines formal descriptions with graphical presentations and encourages readers to interact by creating visual solutions for science-related concepts and presenting data. This reference is essential for researchers, computer scientists, and academics focusing on the integration of science, technology, computing, art, and mathematics for visual problem solving.

A theory of the neural bases of aesthetic experience across the arts, which draws on the tools of both cognitive neuroscience and traditional humanist inquiry. In Feeling Beauty, G. Gabrielle Starr argues that understanding the neural underpinnings of aesthetic experience can reshape our conceptions of aesthetics and the arts. Drawing on the tools of both cognitive neuroscience and traditional humanist inquiry, Starr shows that neuroaesthetics offers a new model for understanding the dynamic and changing features of aesthetic life, the relationships among the arts, and how individual differences in aesthetic judgment shape the varieties of aesthetic experience. Starr, a scholar of the humanities and a researcher in the neuroscience of aesthetics, proposes that aesthetic experience relies on a distributed neural architecture—a set of brain areas involved in emotion, perception, imagery, memory, and language. More important, it emerges from networked interactions, intricately connected and coordinated brain systems that together form a flexible architecture enabling us to develop new arts and to see the world around us differently. Focusing on the "sister arts" of poetry, painting, and music, Starr builds and tests a neural model of aesthetic experience valid across all the arts. Asking why works that address different senses using different means seem to produce the same set of feelings, she examines particular works of art in a range of media, including a poem by Keats, a painting by van Gogh, a sculpture by Bernini, and Beethoven's Diabelli Variations. Starr's innovative, interdisciplinary analysis is true to the complexities of both the physical instantiation of aesthetics and the realities of artistic representation.

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.