An Annotated Bibliography of Books for Architecture and Mathematics
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Painting by the Numbers: a Porter Postscript
Painting by the Numbers: A Porter Postscript Chris Bartlett Art Department Towson University 8000 York Road Towson, MD, 21252, USA. E-mail: [email protected] Abstract At the 2005 Bridges conference the author presented a paper titled, “Fairfield Porter’s Secret Geometry”. Porter (1907-1975), an important American painter, is known for his “naturalness” and seems to eschew any system of proportioning. This paper briefly traces other influences on Porter’s use of geometry in art and offers an analysis of two more of his paintings to reveal detailed and sophisticated geometric structures based on the Golden Ratio and Dynamic Symmetry. Introduction Artists throughout history have sought a key to beauty in proportioning systems in composition, a procedural method for compositional structure. Starting in the late 19th century there was a general resurgence of interest in geometrical structure as a basis for painting. Artists were researching aids to producing analogous and self-similar areas and repetitions of ratios in assigning the elements of a painting. In the 1920’s in America compositional methods gained new popularity fueled by Matila Ghyka and Jay Hambidge such that Milton Brown was prompted to title a critical article in the Magazine of Art, “Twentieth Century Nostrums: Pseudo-Scientific Theory in American Painting”. [1] More recently there have been growing circles criticizing the hegemony of the Golden Mean as a universal aesthetic panacea. [2] The principle of beauty underlining the application of the Golden Ratio and Dynamic Symmetry proportioning in a composition is not irrefutable, but what seems like a more useful exercise than to debate research in perception of elegant proportion is to look at the works of artists who seem to have fallen under its spell. -
The Dual Language of Geometry in Gothic Architecture: the Symbolic Message of Euclidian Geometry Versus the Visual Dialogue of Fractal Geometry
Peregrinations: Journal of Medieval Art and Architecture Volume 5 Issue 2 135-172 2015 The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry Nelly Shafik Ramzy Sinai University Follow this and additional works at: https://digital.kenyon.edu/perejournal Part of the Ancient, Medieval, Renaissance and Baroque Art and Architecture Commons Recommended Citation Ramzy, Nelly Shafik. "The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry." Peregrinations: Journal of Medieval Art and Architecture 5, 2 (2015): 135-172. https://digital.kenyon.edu/perejournal/vol5/iss2/7 This Feature Article is brought to you for free and open access by the Art History at Digital Kenyon: Research, Scholarship, and Creative Exchange. It has been accepted for inclusion in Peregrinations: Journal of Medieval Art and Architecture by an authorized editor of Digital Kenyon: Research, Scholarship, and Creative Exchange. For more information, please contact [email protected]. Ramzy The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry By Nelly Shafik Ramzy, Department of Architectural Engineering, Faculty of Engineering Sciences, Sinai University, El Masaeed, El Arish City, Egypt 1. Introduction When performing geometrical analysis of historical buildings, it is important to keep in mind what were the intentions -
Assessing Alexander's Later Contributions to a Science of Cities
Review Assessing Alexander’s Later Contributions to a Science of Cities Michael W. Mehaffy KTH Royal Institute of Technology, 114 28 Stockholm, Sweden; mmehaff[email protected] or michael.mehaff[email protected] Received: 23 April 2019; Accepted: 28 May 2019; Published: 30 May 2019 Abstract: Christopher Alexander published his longest and arguably most philosophical work, The Nature of Order, beginning in 2003. Early criticism assessed that text to be a speculative failure; at best, unrelated to Alexander’s earlier, mathematically grounded work. On the contrary, this review presents evidence that the newer work was a logically consistent culmination of a lifelong and remarkably useful inquiry into part-whole relations—an ancient but still-relevant and even urgent topic of design, architecture, urbanism, and science. Further evidence demonstrates that Alexander’s practical contributions are remarkably prodigious beyond architecture, in fields as diverse as computer science, biology and organization theory, and that these contributions continue today. This review assesses the potential for more particular contributions to the urban professions from the later work, and specifically, to an emerging “science of cities.” It examines the practical, as well as philosophical contributions of Alexander’s proposed tools and methodologies for the design process, considering both their quantitative and qualitative aspects, and their potential compatibility with other tools and strategies now emerging from the science of cities. Finally, it highlights Alexander’s challenge to an architecture profession that seems increasingly isolated, mired in abstraction, and incapable of effectively responding to larger technological and philosophical challenges. Keywords: Christopher Alexander; The Nature of Order; pattern language; structure-preserving transformations; science of cities 1. -
The Patterns of Architecture/T3xture
THE PATTERNS OF ARCHITECTURE NIKOS A. SALINGAROS Published in Lynda Burke, Randy Sovich, and Craig Purcell, Editors: T3XTURE No. 3, CreateSpace Independent Publishing Platform, 2016, pages 7-24. EDITORS’ INTRODUCTION Pattern theory has not as yet transformed architectural practice—despite the acclaim for A Pattern Language, 1 Christopher Alexander’s book, which introduced and substantiated the theory. However, it has generated a great amount of far-ranging, supportive scholarship. In this essay Nikos Salingaros expands the scope of the pattern types under consideration, and explicates some of the mathematical, scientific and humanistic justification for the pattern approach. The author also argues for the manifest superiority of the pattern approach to design over Modernist and contemporary theories of the last one hundred years. To a great extent Dr. Salingaros’s conviction rests on the process and goals of the pattern language method which have as their basis the fundamental realities of the natural world: the mathematics of nature (many that have been studied since the beginning of human history); the process of organic development; and the ideal structural environment for human activity. For Salingaros, Alexander, et al. aesthetics in Architecture derive from these principles rather than from notions of style or artistic inspiration. AUTHOR’S INTRODUCTION — KEY PATTERN CONCEPTS Pattern. A pattern is a discovered organization of space, and also a coherent merging of geometry with human actions. In common usage “pattern” has an expansive definition. In Architecture “pattern” often equates with “solution”. In any discussion of architectural pattern theory the word “pattern” itself is used repeatedly, often with reference to somewhat different concepts. -
Working with Fractals a Resource for Practitioners of Biophilic Design
WORKING WITH FRACTALS A RESOURCE FOR PRACTITIONERS OF BIOPHILIC DESIGN A PROJECT OF THE EUROPEAN ‘COST RESTORE ACTION’ PREPARED BY RITA TROMBIN IN COLLABORATION WITH ACKNOWLEDGEMENTS This toolkit is the result of a joint effort between Terrapin Bright Green, Cost RESTORE Action (REthinking Sustainability TOwards a Regenerative Economy), EURAC Research, International Living Future Institute, Living Future Europe and many other partners, including industry professionals and academics. AUTHOR Rita Trombin SUPERVISOR & EDITOR Catherine O. Ryan CONTRIBUTORS Belal Abboushi, Pacific Northwest National Laboratory (PNNL) Luca Baraldo, COOKFOX Architects DCP Bethany Borel, COOKFOX Architects DCP Bill Browning, Terrapin Bright Green Judith Heerwagen, University of Washington Giammarco Nalin, Goethe Universität Kari Pei, Interface Nikos Salingaros, University of Texas at San Antonio Catherine Stolarski, Catherine Stolarski Design Richard Taylor, University of Oregon Dakota Walker, Terrapin Bright Green Emily Winer, International Well Building Institute CITATION Rita Trombin, ‘Working with fractals: a resource companion for practitioners of biophilic design’. Report, Terrapin Bright Green: New York, 31 December 2020. Revised June 2021 © 2020 Terrapin Bright Green LLC For inquiries: [email protected] or [email protected] COVER DESIGN: Catherine O. Ryan COVER IMAGES: Ice crystals (snow-603675) by Quartzla from Pixabay; fractal gasket snowflake by Catherine Stolarski Design. 2 Working with Fractals: A Toolkit © 2020 Terrapin Bright Green LLC -
The Impacts of Symmetry in Architecture and Urbanism: Toward a New Research Agenda
buildings Article The Impacts of Symmetry in Architecture and Urbanism: Toward a New Research Agenda Michael W. Mehaffy Centre for the Future of Places, KTH Royal Institute of Technology, 114 28 Stockholm, Sweden; mmehaff[email protected] Received: 7 November 2020; Accepted: 15 December 2020; Published: 19 December 2020 Abstract: Architecture has an ancient relationship to mathematics, and symmetry—in the broad sense of the term—is a core topic of both. Yet the contemporary application of theories of symmetry to architecture and built environments is a surprisingly immature area of research. At the same time, research is showing a divergence between the benefits of and preferences for natural environments on the one hand, and built environments on the other, demonstrating relatively deleterious effects of many contemporary built environments. Yet the research cannot yet pinpoint the actual geometric factors of architecture and urbanism that could produce such an important divergence. This paper explores this research gap, surveying the literature across a range of fields, and assessing current evidence for the impacts of symmetry in the built environment upon human perception and well-being. As an emerging case study, it considers the recent work by Christopher Alexander and Nikos Salingaros, two trained mathematicians who have made notable contributions to architecture and urbanism. The conclusion proposes a new research agenda toward further development of this immature subject area. Keywords: symmetry; aesthetics; geometry; biophilia; environmental preference 1. Introduction The application of mathematics to architecture is very likely as old as architecture itself [1]. From the use of arithmetic to measure lengths, to the calculation of squares and angles, to the complex analysis of structural loading capacities, mathematics has served architecture as an essential toolset to improve quality and performance. -
Conversations with Alexander
Conversations with Alexander David West, Transcendence Corporation _______________________________________________________________________ This is an essay about the author’s interaction with ideas advanced by Christopher Alexander. The essay has three inter-related themes: Alexander’s ideas and how they influenced the author’s own work; Alexander’s impact (or lack of it) on software development in general; and the Patterns Movement that Alexander is credited for inspiring. ACM Reference Format: West, D.. 2012. Conversations With Alexander. ACM 21 pages. Our first, meeting was in 1987. The meeting place, Notes on the Synthesis of Form (Notes) - a small book with a stark black cover and white text; an edited version of Alexander’s doctoral thesis twenty years earlier. I was a graduate student at the University of Wisconsin – Madison. I had returned to school (leaving Macalester the second semester of my senior year) two years earlier (1985) after seventeen years working as a software development professional. By 1987 I had finished my undergraduate credits and completed two masters degrees, one in computer science and the other in cultural anthropology and was working on my Ph.D., ostensibly in cognitive anthropology but really interdisciplinary. I had three anthropologists, two computer scientists, a linguist and a psychologist as my dissertation committee. Although my CS Masters was in the area of artificial intelligence, I was convinced that the computational model of cognition was, not only wrong, but silly. It seemed that the model willfully ignored 99% of cognition to focus only on the simplest elements, those that a computer could simulate. My dissertation research was focused on devising a model of cognition that at least incorporated the role of culture. -
Influences of the Ideas of Jay Hambidge on Art and Design
Computers Math. Appltc. Vol. 17, No. 4-6, pp. 1001-1008, 1989 0097-4943/89 $3.00+0.00 Printed in Great Britain. All rights reserved Copyright © 1989 Pergamon Press plc INFLUENCES OF THE IDEAS OF JAY HAMBIDGE ON ART AND DESIGN H. J. McWmNNm Department of Design, University of Maryland, College Park, MD 20742, U.S.A. AImtraet--The system of dynamic symmetry, as an approach to decision-making in design, by Jay Hambidge in the early 1920s had a strong influence on industrial design as well as upon the work of painters. This paper will review the design theories of Jay Hambidge and dynamic symmetry in terms of the use of proportions in design which are humanistically based upon the proportions of the human body. Recent research in the general area known as the golden section hypothesis will be reviewed as a means of justification not only for Hambidge's theory of proportions in design but as a validation for recent ideas in design, especially those of Robert Venturi. The paper will demonstrate the utility of studies from the behaviorial sciences for questions of design history as well as for present-day design theory and practice. The work of contemporary artists and designers will be shown to demonstrate that these ideas, the golden section and dynamic symmetry, while popular in the 1920s, have a renewed sense of relevance to current ideas and approaches in design theory. The influence upon industrial design, while it may not be clear as say the influence of dynamic symmetry or the work of Bellows or Rothko, is nevertheless also quite clear. -
Aesthetical Issues of Leonardo Da Vinci's and Pablo Picasso's
heritage Article Aesthetical Issues of Leonardo Da Vinci’s and Pablo Picasso’s Paintings with Stochastic Evaluation G.-Fivos Sargentis * , Panayiotis Dimitriadis and Demetris Koutsoyiannis Laboratory of Hydrology and Water Resources Development, School of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 9, 157 80 Zographou, Greece; [email protected] (P.D.); [email protected] (D.K.) * Correspondence: fi[email protected] Received: 7 April 2020; Accepted: 21 April 2020; Published: 25 April 2020 Abstract: A physical process is characterized as complex when it is difficult to analyze or explain in a simple way. The complexity within an art painting is expected to be high, possibly comparable to that of nature. Therefore, constructions of artists (e.g., paintings, music, literature, etc.) are expected to be also of high complexity since they are produced by numerous human (e.g., logic, instinct, emotions, etc.) and non-human (e.g., quality of paints, paper, tools, etc.) processes interacting with each other in a complex manner. The result of the interaction among various processes is not a white-noise behavior, but one where clusters of high or low values of quantified attributes appear in a non-predictive manner, thus highly increasing the uncertainty and the variability. In this work, we analyze stochastic patterns in terms of the dependence structure of art paintings of Da Vinci and Picasso with a stochastic 2D tool and investigate the similarities or differences among the artworks. Keywords: aesthetic of art paintings; stochastic analysis of images; Leonardo Da Vinci; Pablo Picasso 1. Introduction The meaning of beauty is linked to the evolution of human civilization, and the analysis of the connection between the observer and the beauty in art and nature has always been of high interest in both philosophy and science. -
14 Patterns of Biophilic Design
14 PATTERNS OF BIOPHILIC DESIGN IMPROVING HEALTH & WELL-BEING IN THE BUILT ENVIRONMENT “…the enjoyment of scenery employs the mind without fatigue and yet exercises it, tranquilizes it and yet enlivens it; and thus, through the influence of the mind over the body, gives the effect of refreshing rest and reinvigoration to the whole system.” Frederick Law Olmsted, 1865 Introduction to Yosemite and the Mariposa Grove: A Preliminary Report 14 Patterns of Biophilic Design ACKNOWLEDGEMENTS This paper was supported by Terrapin Bright Green, LLC. We thank Alice Hartley for editorial assistance, Allison Bernett and Cas Smith for production assistance, the Review Committee and Contributors for their technical guidance and expertise, Georgy Olivieri for her relentless energy and dedication to spreading the word, Stefano Serafini and the International Society of Biourbanism for providing guidance and encouragement. CO-AUTHORS William Browning, Hon. AIA Terrapin Bright Green Catherine Ryan Terrapin Bright Green Joseph Clancy Pegasus Planning Group Ltd. REVIEW COMMITTEE Sally Augustin, PhD Design With Science; Research Design Connections Judith Heerwagen, PhD J.H. Heerwagen & Associates; University of Washington, Department of Architecture Lance Hosey, FAIA RTKL CONTRIBUTORS Scott Andrews Terrapin Bright Green Gail Brager, PhD University of California at Berkeley, Center for the Built Environment Zafir Buraei, PhD Pace University, Department of Biology and Health Sciences Nancy Clanton, PE, FIES, IALD Clanton & Associates, Inc. Chris Garvin, AIA Terrapin -
Architecture, Patterns, and Mathematics Nikos A. Salingaros
Nexus Esecutivo 19-01-2004 9:18 Seite 75 Nikos A. Architecture, Patterns, Salingaros and Mathematics Nikos Salingaros posits the importance of architectural pattern in man’s intellectual development, examining how twentieth century architectural attitudes towards decoration and pattern have impoverished man’s experience of both mathematics and the built environment. Introduction The traditionally intimate relationship between architecture and mathematics changed in the twentieth century. Architecture students are no longer required to have a mathematical background. While a problem in itself, a far more serious possibility is that contemporary architecture and design may be promoting an anti-mathematical mind-set. The modernist movement suppresses pattern in architecture, and this has profound implications for society as a whole. Mathematics is a science of patterns, and the presence or absence of patterns in our surroundings influences how easily one is able to grasp concepts that rely on patterns. Eliminating patterns from twentieth-century architecture affects our capacity to process and interpret patterns in thought. Mathematics, and the intellectual patterns it embodies, lie outside our contemporary, explicitly anti-pattern architectural world-view. Mathematics teachers are bemoaning the fact that there is less and less interest in mathematics, which has resulted in a declining mathematical capacity among students. This stands in sharp contrast - indeed a contradiction - with the increasing technological advances we are witnessing in our times. Here, it is proposed that an environmental factor might contribute to the overall decline of mathematics in our society. This theory arose from the author’s interest in the theoretical basis behind architectural styles from different periods and regions. -
Towards Human-Oriented Design, Architecture and Urbanism: Shifts in Education and Practice
Towards human-oriented design, architecture and urbanism: shifts in education and practice. Item Type Thesis or dissertation Authors Tracada, Eleni Publisher University of Derby Download date 23/09/2021 20:04:21 Link to Item http://hdl.handle.net/10545/582094 Towards human-oriented design, architecture and urbanism: shifts in education and practice. Faculty of Arts, Design & Technology School of Engineering and Technology Division of Built Environment May 2015 Eleni Tracada A submission in partial fulfilment of the requirements of the University of Derby for the award of the degree of Doctor of Philosophy or Master of Philosophy based upon Published Works 1 Contents Abstract p. 3 List of figures p. 5 1. Introduction p. 9 1.1 Background p. 9 1.2 The ‘big themes’ and experiences from the 1970s until today p. 13 2. Links of the publications with the ‘big themes’ of an intellectual journey p. 34 2.1 Publication of materials contributing to innovative behavioural and cognitive processes of learning p. 34 2.2 Publication of materials on architecture and urbanism with reference to social and scientific frameworks p. 52 3. Recent editorial work and research – Future opportunities p. 69 4. Conclusions p. 70 References p. 72 2 Abstract The scope of this piece of work is to reflect upon a series of past and recent publications as well as those in progress referring to innovations in architectural education which has already led and/or might lead to major shifts in future practices. This is an opportunity for the author to reflect on concepts and ideas for the future of architecture which is currently undergoing innovative developments by embracing new theories and enduring professional formation according to contemporary trends.