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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with an elegant lucidity, Devlin shows just why the definition of mathematics as "working with numbers" has been out of date for nearly 2,500 years.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.
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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.
72.01 --- Architectuurtheorie over de Moderne Beweging --- Architectuur en wiskunde architectuur en wetenschap --- Architectuur 1ste h. 20ste eeuw --- Modernisme --- Architectuur theorie, filosofie, esthetica --- Modern Movement (Architecture) --- Modernism (Architecture) --- Modernist architecture --- Modern movement (Architecture). --- Modern movement (Architecture) --- Architecture, Modern --- Mouvement moderne (Architecture) --- Architecture --- International style (Architecture) --- Architectuur ; 1ste h. 20ste eeuw --- Architectuur en wiskunde ; architectuur en wetenschap --- Architectuurtheorie ; over de Moderne Beweging --- Architectuur ; theorie, filosofie, esthetica
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Wiskunde geschiedenis --- Wiskunde : maatschappelijke relevantie --- 511 --- 510 --- 51-73 --- Architectuur ; in de natuur ; zuinigheidsbeginsel --- Architectuur en wiskunde ; architectuur en wetenschap --- Wiskunde ; variatierekening ; optimale vormberekening --- Mathematics--?-73 --- Architectuur ; proportie, symmetrie, harmonie --- Architectonische vormgeving --- Natuurlijke vormen --- out of print --- Architectonische vormgeving. --- Natuurlijke vormen. --- 51-73 Mathematics--?-73 --- Wiskunde ; geschiedenis --- natuur --- structuren --- 53 --- 54 --- $?$90/05 --- 72.013 --- Nature protection --- Science --- Mathematics
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History --- Baroque --- geometry --- Architecture --- architecture [discipline] --- anno 1700-1799 --- anno 1600-1699 --- Architectuurtheorie ; Barok ; geometrie ; harmonie --- Architectuur en wiskunde ; architectuur en wetenschap --- Architectuur en muziek --- 72.034 --- 72.01 --- Architectuurgeschiedenis ; Renaissance ; Barok ; Rococo --- Architectuur ; theorie, filosofie, esthetica --- Architectural design --- Architecture, Baroque --- Geometry in architecture --- Mathematics. --- Architecture [Modern ] --- 17th-18th centuries --- Europe --- Architecture [Baroque ] --- Mathematics --- Architecture, Western (Western countries) --- Building design --- Buildings --- Construction --- Western architecture (Western countries) --- Baroque architecture --- Design and construction --- Art --- Building --- Design --- Structural design --- Composition, proportion, etc. --- Architecture, Primitive --- Géometrie
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Architecture and science --- Architecture and technology --- Architecture et science --- Architecture et sciences --- Architecture et technologie --- Architectuur en technologie --- Architectuur en wetenschap --- Laboratoires --- Laboratoria --- Laboratories --- Laboratories [Scientific ] --- Research buildings --- Science and architecture --- Science et architecture --- Science laboratories --- Sciences et architecture --- Scientific laboratories --- Technologie en architectuur --- Technologie et architecture --- Technology and architecture --- Wetenschap en architectuur --- Architecture and science. --- Architecture and technology. --- Laboratories. --- 727 --- 727.5 --- 5 --- Laboratory facilities --- Science rooms and equipment --- Technology --- Science --- Gebouwen voor wetenschappelijke doeleinden --- Laboratoria (architecuur) --- Onderzoeksinstituten (architectuur) --- Wetenschappen
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churches [buildings] --- Religious architecture --- symbolism [artistic concept] --- Gothic [Medieval] --- Semiotics --- anno 1100-1199 --- anno 1200-1499 --- Western Europe --- 726 --- 726.6 --- 72.033.5 --- 72.033 --- 514 --- Symbolen --- Kathedralen ; symboliek --- architectuur --- religieuze architectuur --- kerken --- kathedralen --- Frankrijk --- beeldhouwkunst --- XXIII --- middeleeuwen --- gotiek --- symboliek --- proportie --- Chartres --- geometrie --- Engeland --- veelhoeken --- driehoeken --- vierkanten --- vijfhoeken --- getallensymboliek --- triangulatuur --- kwadratuur --- planten --- dieren --- platonisme --- kunst en wetenschap --- architectuur en wetenschap --- bouwtechniek --- Amiens --- religieuze gebouwen --- architectuurdetails --- 72.04 --- Kerkelijke bouwkunst --- Religieuze architectuur --- Kathedralen (architectuur) --- Gotiek (architectuur) --- Gotische architectuur --- Middeleeuwen (architectuur) --- Middeleeuwse architectuur --- Geometrie --- Religieuze architectuur ; kathedralen --- architectuur - ornamentiek, architecturale details --- Architecture, Medieval --- Cathedrals --- Symbolism in architecture --- Architectural symbolism --- Signs and symbols in architecture --- Architecture --- Church architecture --- Church buildings --- Middle Ages
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Architectural design. --- Architecture --- Design architectural --- Mathematics. --- Mathématiques --- 72.012/013 --- 51 --- 72.013 --- 514 --- Architectuur en wiskunde ; architectuur en wetenschap --- Wright, Frank Lloyd --- Stedenbouw ; Venetië --- Proportieleer ; gulden snede ; gulden getal --- Kunst en natuur ; mathematische modellen ; fractalen --- Michelangelo ; Rome ; Bibliotheca Laurenziana ; ontleding tegelvloer --- Tegels ; wandtegels ; patrone ; ontleding door R. Penrose --- Alberti, Leon Battista --- Romeinse architectuur ; Rome ; Pantheon ; quadrivium --- Fibonacci cijfers --- Palladio, Andrea --- Afrikaanse kunst en architectuur ; geometrische analyse --- Gulden snede (architectuur) --- Modulaire coordinatie --- Proportie (architectuur) --- Symmetrie (architectuur) --- Wiskunde --- Mathematica --- Architectuur ; proportie, symmetrie, harmonie --- Wiskunde ; geometrie, meetkunde --- Mathématiques --- Architectural design --- Architecture, Western (Western countries) --- Building design --- Buildings --- Construction --- Western architecture (Western countries) --- Art --- Building --- Mathematics --- Design and construction --- Architecture, Primitive
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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.
Architecture --- Architecture et technologie --- Mathématiques --- Conception assistée par ordinateur --- 72.012/013 --- 51 --- Architectuur en wiskunde ; architectuur en wetenschap --- Kunst en wetenschap ; kunst en wiskunde --- Architectuur & technologie --- Virtuele architectuur --- Architectuur en digitale technieken --- Architectuurtheorie ; topologie van de ruimte --- 72.013 --- Ontwerp (architectuur) --- Wiskunde --- Architectuurontwerp --- Architectonisch ontwerp --- Digitale architectuur --- CAAD --- Computer aided architectural design --- Architectuur ; proportie, symmetrie, harmonie --- Architecture and technology --- Space (Architecture) --- Architecture and space --- Space and architectural mass --- Space in architecture --- City planning --- Architecture and mathematics --- Mathematics and architecture --- Technology and architecture --- Technology --- Mathematics --- Composition, proportion, etc. --- Architecture et technologie. --- Mathématiques. --- Conception assistée par ordinateur. --- Negative space (Architecture) --- Mathématiques. --- Conception assistée par ordinateur
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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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