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Connections between mathematics, the arts and architecture
The purpose of this book is to analyse the interdisciplinary aspects of mathematics and geometry in reference to nature, art, and architecture. In Chapter 1, we introduce symmetry and its different meanings. Symmetry is a notion, which has been applied in the arts and architecture to find harmony and beauty. It joins aesthetics and practice, science and economy, mathematics and philosophy. In this chapter, we also analyze the influence of Vitruvius and the concept of old symmetry, received by the Renaissance. It is also interesting to note how in contemporary architecture there is often the presence of the \"break\" of symmetry (for example in the Frank O Gehry's works). Chapter 2 explains how proportions, and in particular, the golden section, has introduced aesthetic canons that have strongly influenced many artists like Polycletus, and architects, from Ictinus to Le Corbusier. In Chapter 3, we discover how curves and spirals find their application in artistic works, for example in Mycenaean jewellery, and architectural works, from the Baroque of Francesco Borromini to the Land Art of Smithson. Chapter 4 presents the importance and influence that Platonic solids and polyhedrons have had on philosophy and art through different historical periods and different cultures. For instance, we look at how Platonic solids are connected to the theory of Empedocles' elements and Hippocrates' theory of humors. Chapter 5 describes surfaces, discovering how different cultures have used them in different manners, including Roman aqueducts, iron bridges, and finally arriving on modern structures that base their forms on hyperboloids and paraboloids. In Chapter 6, we introduce fractal geometry, as a geometry that tries to explain nature's irregular shapes, trying to overcome the limitations imposed by \"old\" Euclidean geometry. We also analyse how fractal geometry has influenced architecture in this century.
eBook
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
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
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
Grassmannians of classical buildings (Algebra and discrete mathematics, vol. 2)
Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results from the geometry of linear groups. The presented methods are applied to some geometric constructions non-related to buildings - Grassmannians of infinite-dimensional vector spaces and the sets of conjugate linear involutions.
The book is self-contained and the requirement for the reader is a knowledge of basic algebra and graph theory. This makes it very suitable for use in a course for graduate students.
eBook
François Blondel
First director of the Académie royale d'architecture, François Blondel established a lasting model for architectural education that helped transform a still largely medieval profession into the one we recognize today.
Most well known for his 1676 urban plan of Paris, Blondel is also celebrated as a mathematician, scientist, and scholar. Few figures are more representative of the close affinity between architecture and the \"new science\" of the seventeenth century.
The first full-length study in English to appear on this polymath, this book adds to the scholarship on early modern architectural history and particularly on French classicism under Louis XIV and his minister Jean-Baptiste Colbert. It studies early modern science and technology, Baroque court culture, and the development of the discipline of architecture.
eBook