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Mathematics, The Science of Patterns : The Search for Order in Life, Mind, and the Universe
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ISBN: 0716750473 9780716750475 0716760223 9780716760221 Year: 1994 Publisher: New York Scientific American Library

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With this fascinating volume, Keith Devlin proves that the guiding principles of some of the most mysterious mathematical topics can be made comprehensible. Writing with an elegant lucidity, Devlin shows just why the definition of mathematics as "working with numbers" has been out of date for nearly 2,500 years. And he demonstrates that far from being too abstract to matter, mathematics is instead an essential and uniquely human endeavor, one that helps us understand the universe and ourselves." "In this century alone, there has been a veritable explosion of mathematical activity. A body of knowledge that in 1900 might have filled 80 volumes now would require nearly 100,000. Fields such as algebra and topology have grown tremendously, while complexity theory, dynamical systems theory, and other new areas have developed. And in the last two decades, a common thread running through the many facets of mathematics has been recognized: mathematicians of all kinds now see their work as the study of patterns - real or imagined, visual or mental, arising from the natural world or from within the human mind." "Devlin uses this basic definition as his central theme, revealing the search for patterns that drives the mathematics of counting (natural numbers), reasoning (language and logic), motion (calculus), shape (geometry, tilings), and position (topology, knots, symmetry). Interweaving historical highlights and current developments, and using a minimum of formulas, he lets readers see into the kind of reasoning that allows mathematicians to create and explore arcane subjects. And he makes clear the many ways mathematics informs our perceptions of reality - both the physical, biological, and social worlds without, and the realm of ideas and thoughts within.

Architectures of time : toward a theory of the event in modernist culture.
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ISBN: 0262611813 0262112604 9780262611817 Year: 2002 Publisher: Cambridge, Mass. London MIT

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An exploration of twentieth-century conceptions of time and their relation to artistic form. In Architectures of Time, Sanford Kwinter offers a critical guide to the modern history of time and to the interplay between the physical sciences and the arts. Tracing the transformation of twentieth-century epistemology to the rise of thermodynamics and statistical mechanics, Kwinter explains how the demise of the concept of absolute time, and of the classical notion of space as a fixed background against which things occur, led to field theory and a physics of the "event." He suggests that the closed, controlled, and mechanical world of physics gave way to the approximate, active, and qualitative world of biology as a model of both scientific and metaphysical explanation.Kwinter examines theory of time and space in Einstein's theories of relativity and shows how these ideas were reflected in the writings of the sculptor Umberto Boccioni, the town planning schema of the Futurist architect Antonio Sant'Elia, the philosophy of Henri Bergson, and the writings of Franz Kafka. He argues that the writings of Boccioni and the visionary architecture of Sant'Elia represent the earliest and most profound deployments of the concepts of field and event. In discussing Kafka's work, he moves away from the thermodynamic model in favor of the closely related one of Bergsonian duree, or virtuality. He argues that Kafka's work manifests a coherent cosmology that can be understood only in relation to the constant temporal flux that underlies it.


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Symboliek in kathedralenbouw.
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ISBN: 9062719031 Year: 2001 Publisher: Den Haag Mirananda

Nexus : architecture and mathematics. II.
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ISBN: 8886888139 Year: 1998 Publisher: Firenze Edizioni dell'Erba

Mathland : from flatland to hypersurfaces.
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ISBN: 9783764301491 376430149X Year: 2004 Publisher: Basel Birkhäuser

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Space "mutates" and is strictly dependent on our scientific concepts. The mutation of these concepts is important because even architecture mutates over time, changing with the various periods and variations in the tools that allow its realization. We can be certain of some of these relationships between the scientific concepts of space and architecture, the relationship between perspective, the architecture of Humanism and the Ptolemaic universe, or that of Cartesian space, of the Mongean projection system and the progressive birth of an architecture that was first a perspective and then more abstract and analytical. But what is happening today? Because if the concept of space has been mutated (and how!) and if the computer technology of this mutation is an agent to at least two or three different powers, then we are in a field of research as rich as it is difficult. We begin to understand the laws and see several possibilities. We are in a "topological" concept of space (we are not interested in the construction of geometric "absolutes" but in systems of families and possible relationships between forms) and are also working to create form in architecture and make spaces actually explorable in more dimensions than just the Cartesian ones.


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De nieuwe mathematica van de hedendaagse architectuur : bouwen in de 21ste eeuw.
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ISBN: 9789068685497 Year: 2010 Publisher: Bussum Thoth

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Keywords

architectuur --- architecture [discipline] --- Architecture --- anno 2000-2099 --- 72.039 --- 72:681.3 --- Architectuur ; 21ste eeuw ; 2000-2010 --- Architectuur ; ontwerpanalyse ; vormanalyse ; 21ste eeuw --- Architectuur en technologie --- Architectuur en wiskunde ; architectuur en wetenschap --- Architectuur ; stedenbouw ; digitale ontwerpen --- Architectuur ; non standard --- 72.012/013 --- 51 --- 72.01 --- architectonisch ontwerp --- architectuur 21e eeuw --- vormanalyse --- -Euclidean algorithm --- 514.12 --- 72.013 --- 721.01 --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Architecture, Western (Western countries) --- Building design --- Buildings --- Construction --- Western architecture (Western countries) --- Art --- Building --- Architectuurgeschiedenis ; 2000 - 2050 --- Architectuur en computerwetenschappen --- Architectonisch ontwerp --- Architectuurontwerp --- Ontwerp (architectuur) --- Digitale architectuur --- CAAD --- Computer aided architectural design --- Mathematica --- Wiskunde --- architectuurtheorie, ontwerp, vormgeving --- Mathematical models --- Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Vormgeving in de architectuur: proporties; afmetingen; harmonische systemen; principes van eenheid, orde, symmetrie --- Architectuurontwerpen. Bouwplannen. Bouwprojecten --- Hedendaagse architectuur. Bouwkunst sinds 1960 --- Design and construction --- 72.039 Hedendaagse architectuur. Bouwkunst sinds 1960 --- 721.01 Architectuurontwerpen. Bouwplannen. Bouwprojecten --- 72.013 Vormgeving in de architectuur: proporties; afmetingen; harmonische systemen; principes van eenheid, orde, symmetrie --- 514.12 Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Architecture, Primitive

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