New Mathematics of Architecture

New Mathematics of Architecture PDF

Author: Jane Burry

Publisher: National Geographic Books

Published: 2012-03-27

Total Pages: 0

ISBN-13: 0500290253

DOWNLOAD EBOOK →

This carefully researched survey examines how architects now use digital tools and physics to build spatial constructs that would have been inconceivable even ten years ago. Architecture has always relied on mathematics to achieve visual harmony, structural integrity, and logical construction. Now digital tools and an increasing interest in physics have given architects the means to describe and build spatial constructs that would have been inconceivable even ten years ago. This carefully researched survey of forty-six international projects offers an overview of how different strategies are being employed through accessible illustrations and clear text. Each section presents case studies of projects by globally recognized architects in diagrams, photographs, and texts.

The New Mathematics of Architecture

The New Mathematics of Architecture PDF

Author: Jane Burry

Publisher:

Published: 2010

Total Pages: 0

ISBN-13: 9780500342640

DOWNLOAD EBOOK →

From chaos and complexity theory to topology, from optimization to datascapes: the design and construction of complex, sublime buildings that will change the way we perceive major structures.

Architecture of Mathematics

Architecture of Mathematics PDF

Author: Simon Serovajsky

Publisher: CRC Press

Published: 2020-08-11

Total Pages: 395

ISBN-13: 042989354X

DOWNLOAD EBOOK →

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture.

The Architecture of Modern Mathematics

The Architecture of Modern Mathematics PDF

Author: J. Ferreiros

Publisher: OUP Oxford

Published: 2006-04-27

Total Pages: 456

ISBN-13: 0191513792

DOWNLOAD EBOOK →

This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.

Architecture and Mathematics in Ancient Egypt

Architecture and Mathematics in Ancient Egypt PDF

Author: Corinna Rossi

Publisher: Cambridge University Press

Published: 2004-04-15

Total Pages: 400

ISBN-13: 1107320518

DOWNLOAD EBOOK →

In this fascinating study, architect and Egyptologist Corinna Rossi analyses the relationship between mathematics and architecture in ancient Egypt by exploring the use of numbers and geometrical figures in ancient architectural projects and buildings. While previous architectural studies have searched for abstract 'universal rules' to explain the history of Egyptian architecture, Rossi attempts to reconcile the different approaches of archaeologists, architects and historians of mathematics into a single coherent picture. Using a study of a specific group of monuments, the pyramids, and placing them in the context of their cultural and historical background, Rossi argues that theory and practice of construction must be considered as a continuum, not as two separated fields, in order to allow the original planning process of a building to re-emerge. Highly illustrated with plans, diagrams and figures, this book is essential reading for all scholars of Ancient Egypt and the architecture of ancient cultures.

Formulations

Formulations PDF

Author: Andrew Witt

Publisher: MIT Press

Published: 2022-01-11

Total Pages: 433

ISBN-13: 0262543001

DOWNLOAD EBOOK →

An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century. In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.

The Mathematics of the Ideal Villa and Other Essays

The Mathematics of the Ideal Villa and Other Essays PDF

Author: Colin Rowe

Publisher: MIT Press

Published: 1982-09-14

Total Pages: 244

ISBN-13: 9780262680370

DOWNLOAD EBOOK →

This collection of an important architectural theorist's essays considers and compares designs by Palladio and Le Corbusier, discusses mannerism and modern architecture, architectural vocabulary in the 19th century, the architecture of Chicago, neoclassicism and modern architecture, and the architecture of utopia.

A Pattern Language

A Pattern Language PDF

Author: Christopher Alexander

Publisher: Oxford University Press

Published: 2018-09-20

Total Pages:

ISBN-13: 0190050357

DOWNLOAD EBOOK →

You can use this book to design a house for yourself with your family; you can use it to work with your neighbors to improve your town and neighborhood; you can use it to design an office, or a workshop, or a public building. And you can use it to guide you in the actual process of construction. After a ten-year silence, Christopher Alexander and his colleagues at the Center for Environmental Structure are now publishing a major statement in the form of three books which will, in their words, "lay the basis for an entirely new approach to architecture, building and planning, which will we hope replace existing ideas and practices entirely." The three books are The Timeless Way of Building, The Oregon Experiment, and this book, A Pattern Language. At the core of these books is the idea that people should design for themselves their own houses, streets, and communities. This idea may be radical (it implies a radical transformation of the architectural profession) but it comes simply from the observation that most of the wonderful places of the world were not made by architects but by the people. At the core of the books, too, is the point that in designing their environments people always rely on certain "languages," which, like the languages we speak, allow them to articulate and communicate an infinite variety of designs within a forma system which gives them coherence. This book provides a language of this kind. It will enable a person to make a design for almost any kind of building, or any part of the built environment. "Patterns," the units of this language, are answers to design problems (How high should a window sill be? How many stories should a building have? How much space in a neighborhood should be devoted to grass and trees?). More than 250 of the patterns in this pattern language are given: each consists of a problem statement, a discussion of the problem with an illustration, and a solution. As the authors say in their introduction, many of the patterns are archetypal, so deeply rooted in the nature of things that it seemly likely that they will be a part of human nature, and human action, as much in five hundred years as they are today.

Math and Architectures of Deep Learning

Math and Architectures of Deep Learning PDF

Author: Krishnendu Chaudhury

Publisher: Simon and Schuster

Published: 2024-05-21

Total Pages: 550

ISBN-13: 1638350809

DOWNLOAD EBOOK →

Shine a spotlight into the deep learning “black box”. This comprehensive and detailed guide reveals the mathematical and architectural concepts behind deep learning models, so you can customize, maintain, and explain them more effectively. Inside Math and Architectures of Deep Learning you will find: Math, theory, and programming principles side by side Linear algebra, vector calculus and multivariate statistics for deep learning The structure of neural networks Implementing deep learning architectures with Python and PyTorch Troubleshooting underperforming models Working code samples in downloadable Jupyter notebooks The mathematical paradigms behind deep learning models typically begin as hard-to-read academic papers that leave engineers in the dark about how those models actually function. Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. Written by deep learning expert Krishnendu Chaudhury, you’ll peer inside the “black box” to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. Foreword by Prith Banerjee. About the technology Discover what’s going on inside the black box! To work with deep learning you’ll have to choose the right model, train it, preprocess your data, evaluate performance and accuracy, and deal with uncertainty and variability in the outputs of a deployed solution. This book takes you systematically through the core mathematical concepts you’ll need as a working data scientist: vector calculus, linear algebra, and Bayesian inference, all from a deep learning perspective. About the book Math and Architectures of Deep Learning teaches the math, theory, and programming principles of deep learning models laid out side by side, and then puts them into practice with well-annotated Python code. You’ll progress from algebra, calculus, and statistics all the way to state-of-the-art DL architectures taken from the latest research. What's inside The core design principles of neural networks Implementing deep learning with Python and PyTorch Regularizing and optimizing underperforming models About the reader Readers need to know Python and the basics of algebra and calculus. About the author Krishnendu Chaudhury is co-founder and CTO of the AI startup Drishti Technologies. He previously spent a decade each at Google and Adobe. Table of Contents 1 An overview of machine learning and deep learning 2 Vectors, matrices, and tensors in machine learning 3 Classifiers and vector calculus 4 Linear algebraic tools in machine learning 5 Probability distributions in machine learning 6 Bayesian tools for machine learning 7 Function approximation: How neural networks model the world 8 Training neural networks: Forward propagation and backpropagation 9 Loss, optimization, and regularization 10 Convolutions in neural networks 11 Neural networks for image classification and object detection 12 Manifolds, homeomorphism, and neural networks 13 Fully Bayes model parameter estimation 14 Latent space and generative modeling, autoencoders, and variational autoencoders A Appendix