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Geometric Traces: from Historical Interpretations to Complex Constructions
This letter from the editor introduces Vol. 26(2) of the
Nexus Network Journal: Architecture and Mathematics
. The research in this issue addresses two broad themes: the interpretation of historic buildings, ornamentation and materials, and the construction of complex, curvilinear architectural forms. The methods used in this issue range from archaeological surveys and ballistics studies to computational approaches, such as parametric modelling and machine learning. The common thread connecting the work is how geometric properties, some hidden, others more overt, can be used to create new architectural knowledge and applications. Chronologically, the research topics in this issue span from the more than 2000-year-old tombs of the Nabataean Necropolis to contemporary computer-controlled construction processes.
Journal Article
Mathematical excursions to the world’s great buildings
From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect.
Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry.
Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings.
eBook
Geometric Taxonomy
Geometric Taxonomy gets closer to the geometries of Carlos Ferrater and OAB that are present in timeless architecture, those that are explicit in the great treatises, those that dazzled us with \"the correct and magnificent wise play of forms under the light\", the elemental forms that inspired modernity a hundred years ago.
eBook
3D thinking in design and architecture : from antiquity to the future
The geometric foundations, forms, and patterns in today?s architecture, design and, decorative arts can trace their origins in past cultures. From humankind?s first path-like doodles on cave walls through to the higher abstractions developed to make accurate measurements and predictions, the three-dimensional forms we design and build have always been dependent on available materials, human needs, and the limits of our imaginations.00'3D Thinking in Design and Architecture' tells the story of the intimate relationship between geometry, mathematics and man-made design throughout human history, from the Neolithic period through the Indian, Egyptian, Babylonian, Chinese, Greek, Celtic, Islamic and Renaissance cultures, to the present and the possible future. Presenting key principles that can be applied across all design disciplines, design expert Roger Burrows relates how geometry as a visual language has evolved to meet our needs, initiated new technologies, and changed the way we think about the world around us. With a wealth of original artwork by the author to explain his ideas, this book will be an essential reference and source of inspiration for students and design professionals.
Book
Morphing : a guide to mathematical transformations for architects and designers
Cylinders, spheres and cubes are a small handful of shapes that can be defined by a single word. However, most shapes cannot be found in a dictionary. They belong to an alternative plastic world defined by trigonometry: a mathematical world where all shapes can be described under one systematic language and where any shape can transform into another.This visually striking guidebook clearly and systematically lays out the basic foundation for using these mathematical transformations as design tools. It is intended for architects, designers, and anyone with the curiosity to understand the link between shapes and the equations behind them.
eBook
Fractal architecture : organic design philosophy in theory and practice
Throughout history, nature has served as an inspiration for architecture and designers have tried to incorporate the harmonies and patterns of nature into architectural form. Alberti, Charles Renee Macintosh, Frank Lloyd Wright, and Le Courbusier are just a few of the well- known figures who have taken this approach and written on this theme. With the development of fractal geometry--the study of intricate and interesting self- similar mathematical patterns--in the last part of the twentieth century, the quest to replicate nature's creative code took a stunning new turn. Using computers, it is now possible to model and create the organic, self-similar forms of nature in a way never previously realized.
In Fractal Architecture, architect James Harris presents a definitive, lavishly illustrated guide that explains both the \"how\" and \"why\" of incorporating fractal geometry into architectural design.
eBook
A novel conflict-free parallel memory access scheme for FFT constant geometry architectures
In this paper, a parallel conflict-free access scheme for a constant geometry architecture which is unlike the previous schemes is proposed. The proposed method only uses one modular addition operation, and does not involve complicated operations, thus reducing the hardware complexity of address generation. Because of the reduction of the combinational logic which is used to generate the access address, the scheme also reduces the time delay and accordingly improves the executable frequency of fast Fourier transform （FFT） processors. In the scheme, we use an arbitrary radix, i.e., radix-r, to implement the scheme. The scheme is not only applicable to radix-r FFT processors with one butterfly unit, but is also suitable for FFT processors with multiple butterfly units. Because the same architecture is used for every stage of the constant geometry, it can enhance the flexibility of the FFT implementation. Finally, we analyze the resource costs and time delay of the proposed method, and the results verify the advantages of the proposed scheme.
Journal Article