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Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
International Series in Modern Applied Mathematics and Computer Science, Volume 10: Symmetry: Unifying Human Understanding provides a tremendous scope of "symmetry, covering subjects from fractals through court dances to crystallography and literature. This book discusses the limits of perfection, symmetry as an aesthetic factor, extension of the Neumann-Minnigerode-Curie principle, and symmetry of point imperfections in solids. The symmetry rules for chemical reactions, matching and symmetry of graphs, mosaic patterns of H. J. Woods, and bilateral symmetry in insects are also elaborated. This text likewise covers the crystallographic patterns, Milton's mathematical symbol of theodicy, symmetries of soap films, and gapon formalism. This volume is a good source for researchers and specialists concerned with symmetry.
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in OC Mathematics, Chemistry, and Astronomy OCo Professional and ReferenceOCO in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. Contents: Proportion in Architecture; Similarity; The Golden Mean; Graphs; Tilings with Polygons; Two-Dimensional Networks and Lattices; Polyhedra: Platonic Solids; Transformation of the Platonic Solids I; Transformation of the Platonic Solids II; Polyhedra: Space Filling; Isometries and Mirrors; Symmetry of the Plane. Readership: Polytechnic students, architects, designers, mathematicians and general readers."
In this groundbreaking book, Charissa Terranova unearths a forgotten narrative of modernism, which charts the influence that biology, General Systems Theory and cybernetics had on art in the twentieth century. From kinetic and interactive art to early computer art and installations spanning an entire city, she shows that the digital image was a rich and expansive artistic medium of modernism. This book links the emergence of the digital image to the dispersion of biocentric aesthetic philosophies developed by Bauhaus pedagogue Laszlo Moholy-Nagy, from 1920s Berlin to the Massachusetts Institute of Technology in the 1970s. It uncovers seminal but overlooked references to biology, the organism, feedback loops, emotions and the Gestalt, along with an intricate genealogy of related thinkers across disciplines. Terranova interprets anew major art movements such as the Bauhaus, Op Art and Experiments in Art and Technology (E.A.T.), by referencing contemporary insights from architects, embryologists, electrical engineers and computer scientists, among others.This book reveals the complex connections between visual culture, science and technology that comprise the deep history of twentieth-century art.
The demand for math and science skills in our technology-driven world is at a premium, and yet U.S. students continue to lag behind many other industrialized countries in these areas. This book, based on studies conducted on 8000 elementary school-aged children, proposes that not only is there a relationship between music and math comprehension, but that music can be utilized to heighten higher brain function and improve math skills. The enclosed CD-Rom includes (1) a recording of Allegro con spirito from Sonata for Two Pianos in D Major (K. 448), by Wolfgang Amadeus Mozart, performed by Murray Perahia and Radu Lupu, courtesy of Sony ClassicalTM, and (2) a descriptive interactive version of S.T.A.R.TM (Spatial-Temporal Animation Reasoning) software program. While this book's discussion of the breakthroughs in understanding of spatial-temporal reasoning abilities will be of particular interest to neuroscientists and cognitive researchers, the book is also accessible to parents and educators. Presents the theory that music exercises higher brain function and can enhance math comprehension Details how music training coupled with special-temporal reasoning (thinking in pictures) can dramatically impact a child's ability to understand and master math Includes an interactive CD-ROM with math games
Conceptualism and Materiality. Matters of Art and Politics underscores the significance of materials and materiality within Conceptual art and conceptualism more broadly. It challenges the notion of conceptualism as an idea-centered, anti-materialist enterprise, and highlights the political implications thereof. The essays focus on the importance of material considerations for artists working during the 1960s and 1970s in different parts of the world. In reconsidering conceptualism’s neglected material aspects, the authors reveal the rich range of artistic inquiries into theoretical and political notions of matter and material. Their studies revise and diversify the account of this important chapter in the history of twentieth-century art - a reassessment that carries wider implications for the study of art and materiality in general .
How Gyorgy Kepes, the last disciple of Bauhaus modernism, became the single most significant artist within a network of scientific experts and elites. Gyorgy Kepes (1906–2001) was the last disciple of Bauhaus modernism, an acolyte of László Moholy-Nagy and a self-styled revolutionary artist. But by midcentury, transplanted to America, Kepes found he was trapped in the military-industrial-aesthetic complex. In this first book-length study of Kepes, John Blakinger argues that Kepes, by opening the research laboratory to the arts, established a new paradigm for creative practice: the artist as technocrat. First at Chicago's New Bauhaus and then for many years at MIT, Kepes pioneered interdisciplinary collaboration between the arts and sciences—what he termed “interthinking” and “interseeing.” Kepes and his colleagues—ranging from metallurgists to mathematicians—became part of an important but little-explored constellation: the Cold War avant-garde. Blakinger traces Kepes's career in the United States through a series of episodes: Kepes's work with the military on camouflage techniques; his development of a visual design pedagogy, as seen in the exhibition The New Landscape and his book The New Landscape in Art and Science; his encyclopedic Vision + Value series; his unpublished magnum opus, the Light Book; the Center for Advanced Visual Studies (CAVS), an art-science research institute established by Kepes at MIT in 1967; and the Center's proposals for massive environmental installations that would animate the urban landscape. CAVS was entangled in the antiwar politics of the late 1960s, as many students and faculty protested MIT's partnerships with defense contractors—some of whom had ties to the Center. In attempting to “undream” the Bauhaus into existence in the postwar world, Kepes faced profound resistance. Generously illustrated, drawing on the vast archive of Kepes's papers at Stanford and MIT's CAVS Special Collection, this book supplies a missing chapter in our understanding of midcentury modern and Cold War visual culture.
Through a precise and expansive definition of what a pattern is, this book offers ways to understand and use patterns in contemporary design. From the structure of the universe to the print on your grandmother’s couch, patterns are found in a variety of concrete and conceptual phenomena. For architecture, something that so easily traffics between science and taste demands attention, which partially explains patterns’ recent revival across diverse stylistic and intellectual camps. Yet, despite their ubiquity, their resurgence remains un-theorized and their capabilities underutilized. To date no account has been given for their recent proliferation, nor have their various formal and functional capacities been examined. In fact, the relationship between patterns and architecture hasn’t been addressed in almost 30 years. This book fills that gap by tracking the definitions and applications of patterns in a number of fields, and by suggesting how contemporary patterns might be used in design. Drawing on historical material and recent case studies, it gives shape to patterns’ emerging potential. The Architecture of Patterns provides an updated definition of patterns that is at once precise and expansive—one that allows their sensory, ephemeral, and iterative traits to be taken as seriously as their functional, everlasting, and essential ones. Book design by David Carson. Foreword by Sanford Kwinter. Projects by Atelier Manferdini, Bjarke Ingels Group, Ciro Najle, EMERGENT/Thomas Wiscombe, Foreign Office Architects, Jason Payne and Heather Roberge, Herzog and de Meuron, J. Mayer H. Architects, Reiser+Umemoto, Responsive Systems Group, and !ndie architecture.