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Mathematics and the Built Environment

Lee J: Mathematical Thinking and
Properties in Architecture

Mathematical Thinking and Properties in Architecture

Palladio, Le Corbusier, and Eisenman

This open access volume gives a panorama of Shape Computation, exploring its diverse design practices and interdisciplinary applications. Originating in the seminal 1972 article by George Stiny and James Gips&nbsp;that introduced shape grammars as a new computational paradigm, Shape Computation challenges traditional notions of visual and symbolic calculation, particularly in art and design.As we mark the 50th anniversary (1972-2022) of Stiny and Gips’s essay, this volume reflects on Shape Computation's past, present, and future. While this theory has&nbsp;flourished&nbsp;in recent years&nbsp;at the Massachusetts Institute of Technology (MIT), contributions and applications have come from institutions globally. This approach offers an alternative paradigm for design computing, emphasizing generative descriptions through shapes and rules over symbolic instructions.With examples spanning shape grammars, art, architecture, design theory, and more, this volume provides insights into the evolution and significance of this computational approach. Experts and students will appreciate it as a comprehensive introduction to Shape Computation and a valuable historical reference.

Fifty Years, 1972–2022

Shape Computation

This collection of essays reflects the author's decades-long dedication to studying the interplay between mechanics and architecture. It explores how advancements in mechanics have influenced architectural innovation and how the need for new architectural solutions has driven theoretical progress in engineering. By examining the historical roots of these fields, these essays provide a deep analysis of key developments.

This interdisciplinary work will appeal to scholars, students, and anyone interested in the complex relationship between the theoretical and practical aspects of architecture and civil engineering.

The Mathematical Search for Stability in Architecture

Between Mechanics and Architecture

This book presents the first detailed mathematical analysis of the social, cognitive and experiential properties of Modernist domestic architecture.The Modern Movement in architecture, which came to prominence during the first half of the twentieth century, may have been famous for its functional forms and machine-made aesthetic, but it also sought to challenge the way people inhabit, understand and experience space. Ludwig Mies van der Rohe’s buildings were not only minimalist and transparent, they were designed to subvert traditional social hierarchies. Frank Lloyd Wright’s organic Modernism not only attempted to negotiate a more responsive relationship between nature and architecture, but also shape the way people experience space. Richard Neutra’s Californian Modernism is traditionally celebrated for its sleek, geometric forms, but his intention was to use design to support a heightened understanding of context. Glenn Murcutt’s pristine pavilions, seemingly the epitome ofregional Modernism, actually raise important questions about the socio-spatial structure of architecture. Rather than focussing on form or style in Modernism, this book examines the spatial, social and experiential properties of thirty-seven designs by Wright, Mies, Neutra and Murcutt. The computational and mathematical methods used for this purpose are drawn from space syntax, isovist geometry and graph theory. The specific issues that are examined include: the sensory and emotional appeal of space and form; shifting social and spatial structures in architectural planning; wayfinding and visual understanding; and the relationship between form and program.

Architectural Analysis Using Space Syntax and Isovists

The Mathematics of the Modernist Villa

This book deals with the genre of geometric design in the Islamic sphere. Part I presents an overview of Islamic history, its extraordinary spread from the Atlantic to the borders of China in its first century, its adoption of the cultural outlook of the older civilisations that it conquered (in the Middle East, Persia and Central Asia), including their philosophical and scientific achievements - from which it came to express its own unique and highly distinctive artistic and architectural forms. Part II represents the mathematical analysis of Islamic geometric designs.&nbsp; The presentation offers unlimited precision that allows software to reconstruct the design vision of the original artist. This book will be of interest to Islamic academics, mathematicians as well as to artists &amp; art students.

Islamic Design: A Mathematical Approach

Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic andpersonal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.

The Fractal Dimension of Architecture

Im Zentrum dieses Buches über Le Corbusier (1887-1965) steht das vor der Architektur: Das künstlerische Experiment im Atelier der geduldigenForschung, wie diese Überfigur der architektonischen Moderne seinen Arbeitsprozess auch bezeichnete. Forschen bedeutete für ihn das Herantasten an die architektonische Form in Studien und Skizzen und die künstlerische Auseinandersetzung mit Form und Farbe, Flächen und Volumen, Komposition und Raum. Es bedeutete aber auch das Studium der Quellen, die in den kreativen Prozess einflossen - von Fundstücken am Strand bis zur Architektur der Antike. Für Le Corbusier beinhaltete das Entwerfen, Dinge zu ordnen: «Créer une architecture, c'est mettre en ordre». Durch Ordnung die Welt zu gestalten - und so dem Chaos und der Instabilität Einhalt zu gebieten -, sah er als eine Grundaufgabe von Kunst und Architektur mit jahrtausendealter Tradition.
 Der Band bietet eine thematische Übersicht über das künstlerische und gestalterische Schaffen Le Corbusiers über alle Schaffensperioden hinweg. Er beleuchtet einen bisher wenig berücksichtigten Aspekt seines Wirkens: den Entwurf als Manifestation des räumlichen und gestalterischen Denkens. Reich illustriert und mit Texten ausgewiesener Expertinnen und Experten, öffnet das Buch neue Blickwinkel auf Le Corbusiers Werk und gibt einen umfassenden Einblick in Le Corbusiers Prozess des «Forschens» und Entwerfens.

Die Ordnung der Dinge

Le Corbusier

Wozu wir Mathe im Alltag wirklich brauchen <ul><li>Alles andere als trockene Theorie: Mit diesem Buch kommt Schwung in die Mathematik!</li><li>Einfache Schritt-für-Schritt-Erklärungen und Anwendungen für den Alltag machen Mathe endlich greifbar und anschaulich</li><li>Verblüffendes Mathewissen und Ideen zum Ausprobieren: Wie schätzt man die Größe einer Menschenmenge schnell ab? Und wie knackt man Geheimcodes?</li><li>Spielerisch und mit vielen Alltagsbeispielen erfahren Kinder ab 9 Jahren, warum die ganze Welt aus Mathe besteht und wie sie sie für sich nutzen können</li><li>Locker, einfach, leicht verständlich: Neben faszinierenden Wissensfakten aus der Welt der Mathematik vermittelt dieses Buch auch viele Tricks, wie Mathe den Alltag erleichtern kann und nimmt so die Angst vor komplizierten Rechenaufgaben</li><li>Farbige Diagramme und Illustrationen im Retro-Stil machen diese Wissensreise auch visuell zu einem ganz besonderen Erlebnis</li></ul> Erstaunliches und Verblüffendes aus der Welt der Mathematik Aus Mathe-Muffel wird Mathe-Pro: Denn egal, ob in der Natur, Kunst oder Musik, in der Architektur, Medizin oder Wissenschaft - Mathematik ist überall! Dieses kurzweilige und praktische Buch zeigt, wo uns Mathe überall begegnet und wie sie uns im Alltag sogar das Leben leichter machen kann. In 5 Kapiteln geht es nicht nur auf die spannende Geschichte der Mathematik ein, sondern zeigt auch unterhaltsam, hochästhetisch visualisiert und mit vielen Praxisbeispielen, wie lebendig die Mathematik wirklich ist. Endlich Schwung in der Mathematik! Dieses praktische Mathebuch ist ideal für Mathe-Fans und die, die es werden wollen, und zeigt, dass Mathe wirklich überall ist. Ab 9 Jahren.

So unterhaltsam und nützlich ist Mathe im Alltag. Wozu wir Mathe wirklich brauchen. Für Kinder ab 9 Jahren

Wozu eigentlich Mathe?

Sources and Studies in the History of Mathematics and Physical Sciences

Evolving al-Kāshī’s Approximation to the Sine of One Degree

From Samarqand to Jaipur

This book covers all the standard introductory topics in classical mechanics, for the first part: Statics (the analysis of forces and moments acting on a mechanical system in equilibrium with its environment). Starting from Newton's laws, the necessary and sufficient conditions are formulated for a point/rigid/system to remain in equilibrium. The main problems that may arise in engineering practice are analyzed and numerous problems illustrate the presentation. It is well known that classical mechanics, viewed as a theoretical discipline, possesses an inherent beauty, depth and richness and presents coherence and elegance. This book tries to highlight this beauty and harmony that classical mechanics offers. The long experience of the authors means that the way of presentation is intensively tested in the decades of contact with students. The textbook is mainly addressed to advanced undergraduate and beginning graduate students who are interested in the engineering application of modern methods in classical mechanics. The authors try to use a clear and systematic style to promote a good understanding of the subject. For this part of mechanics, statics, the authors motivated and illustrated each concept, with worked examples. The book intends to provide a thorough coverage of the fundamental principles and techniques of classical mechanics. The text is based on the authors' many years of experience delivering lectures and seminars. Most of the problems are original and will be useful not only for those studying mechanics, but also for those who teach it.

Models in Statics for Engineers

This book offers a comprehensive exploration of the intersection between digital technologies and the steel industry, specifically in Poland. By combining theoretical insights with direct research, it highlights the impact of Industry 4.0 and 5.0 on steel manufacturing and decarbonisation. It is an essential read for professionals and researchers looking to understand how automation, digitisation, and sustainability are transforming the steel sector globally and regionally.Robert Wolny, University of Economics in Katowice, PolandThis book presents the impact of digital transformation&nbsp;and other megatrends on the steel industry, focusing on the digitization of processes, and the automation and robotization of operations in steel companies. Technological innovations in the steel industry are presented, as well as the changes taking place within the supply chains An essential part of the book is the results of direct research, which deal with the transformation of enterprises to smart steel manufacturing. The research was done on the Polish steel market, which is an open market with foreign capital. Exploring a sample of representatives of steel companies that serve both domestic and foreign markets, this book discusses the implementation of the pillars of Industry 4.0 as well as the strategic transformation of the steel industry.Bożena Gajdzik&nbsp;is an Associate Professor at the Department of Industrial Informatics at the Silesian University of Technology, Poland. She has been dealing with the economics of business entities, including company management and steel mills. Her output includes 660 publications at national and international publishers, including 30 books about company management and business environment, as well as her monographs about steel industry. Her research is about the restructuring of the Polish steel sector, changes to steel mills in the market in Poland, and now about&nbsp;the transformation of steel industry to Industry 4.0. Scientific interests include economics of business entities, company management, restructuring processes in the steel sector in Poland, changes in the steel industry, competitiveness of steel mills, innovation in steel companies, energy and resources intensity in the steel sector, and smart steel manufacturing. She is ranked in Stanford's Top 2 Scientists list.

A Framework for Steel Enterprises in Poland

Digital Transformation towards Smart Steel Manufacturing

This book provides a pragmatic roadmap for mastering project delivery in civil and infrastructure engineering—one that applies across both developing and industrialized nations. Dr. Arthur L.C. Antoine, an experienced civil engineer, project manager, and researcher, blends real-world case studies with empirical data to scrutinize current project delivery methods and performance. With a focus on the foundational pillars of schedule, cost, and quality—alongside the critical but often overlooked elements of procurement and risk—this book offers a fresh perspective for industry professionals, policymakers, and stakeholders. Through practical insights and rigorous analysis, Dr. Antoine challenges conventional approaches, highlights global best practices, and presents actionable recommendations for delivering infrastructure projects that are successfully delivered with a focus on long-term transformation. The book is ideal for engineers, project managers, public works leaders, and anyone invested in the future of infrastructure development.&nbsp;<ul><li>Blends real-world experience with empirical data to provide a comprehensive analysis of project delivery performance;</li><li>Explores alternative and collaborative project delivery methods, good governance, transparency, accountability and value;</li><li>Uncovers key trends in public procurement and contractor selection, featuring global case studies and practical examples.&nbsp;</li></ul>

A Guide to Successful and Sustainable Project Delivery

Civil Engineering in the Developing World

Chapman Mathematical Notes

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science.

The Mathematical and Philosophical Legacy of Alexander Grothendieck

Lecture Notes in Civil Engineering

Proceedings of DFI-India 2024 13th Annual Conference

Deep Foundations for Infrastructure Development in India, Volume 2

This book contains select proceedings of the 12th annual conference of Deep Foundations Institute of India, DFI-India 2023, held during 05–07 October 2023. The book showcases the advancement in deep foundation technologies through articles on research works and case histories under sub-themes:1) Deep foundation and deep excavation techniques. 2) Sustainability practices in deep foundation industry. 3) Innovative techniques and testing for foundations and&nbsp;geotechnical investigations, monitoring, and performance. 4) Construction and QA/QC of deep foundations including case&nbsp;studies. 5) Ground improvement techniques. 6) Geotechnics for marine, near-shore, and coastal construction. 7) Innovations in experimental and numerical methods in deep foundations and ground improvement. 8) Futuristic technologies in deep foundations—large diameter piles,&nbsp;helical piles, monopiles, tiebacks, driving devices, etc.; legal and&nbsp;contractual aspects of deep foundation construction projects.The articles covered in this book are of immense value to professionals and academicians for improving their work practice.

Proceedings of DFI-India 2023 12th Annual Conference

Deep Foundations for Infrastructure Development in India, Volume 1

This book emphasizes the comprehensive application of sustainability for all sectors of Environment, Energy, Building, and Infrastructure to secure a well-balanced world. Hence, the goal of&nbsp;this book is to define the context of instigation to think through the scientific theories and practical technical applications of the sustainable&nbsp;mechanism to confirm the global sustainability by implementation of the following six themes, Chapter 1: Introduction; Chapter 2: Sustainable Environment; Chapter 3: Sustainable Energy; Chapter 4. Sustainable Building; 5.&nbsp;Sustainable Infrastructure; Chapter 6: Conclusion; which are very much interconnected to secure the global&nbsp;sustainability. Consequently, the importance of the application of sustainability in all sectors of these six sectors has been expedited in this&nbsp;book considering the wise application of technologies by trickling down the advancement thoughts, research, and practices to achieve a broader result to&nbsp;build a better world.<ul><li>Describes sustainability practices for all sectors of environment, energy, building, and infrastructure;</li><li>Stands as a ready reference for researchers, developers, engineers, architects, and policy makers;</li><li>Delineates the importance of sustainable practice to achieve a balanced planet for the next generation.</li></ul>

Sustainable Global Development in Environment, Energy, Building, and Infrastructure

Proceedings of the 2024 Eurasian OpenSees Days

The Minerals, Metals & Materials Series

TMS 2025 154th Annual Meeting & Exhibition Supplemental Proceedings

Mathematical Thinking and Properties in Architecture

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