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The reprint is devoted to the phenomena associated with exact or approximate axial symmetry in different areas of technical physics and mechanical engineering science. How can the symmetry of the problem be used most efficiently for its analysis? Why is the symmetry broken or why is it still approximately retained? These and other questions are discussed based on systems from different fields of engineering.

Symmetry --- History. --- Aesthetics --- Proportion

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The present reprint provides some theoretical results (and their applications) in the fields of mathematical analysis and functional analysis, in which the concept of symmetry plays an essential role. More specifically, various problems are investigated in areas, such as: optimization problems, polynomial approximation on unbounded subsets, moment problems, variational inequalities, evolutionary problems, dynamical systems, generalized convexity, partial differential equations, and special spaces of self-adjoint operators. With various examples and applications to complement and substantiate the mathematical developments, the present reprint is a valuable guide for researchers, engineers, and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science, and economics.

Symmetry. --- Symmetry (Art) --- Form (Aesthetics) --- Proportion (Art) --- Aesthetics --- Proportion

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Architecture --- Architecture --- Composition, proportion, etc.

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Architecture is an experience - with the intellect and with all our senses, in motion, and in use. But in order to actually discuss and assess it with relevance, a clarification of terms is essential in order to avoid the vagueness that often prevails when talking about architecture.This dictionary provides a vocabulary that allows the architecture discourse to go beyond the declaration of constructive relationships or the description of architectonic forms in familiar terms like "roof," "base," "wall," and "axis" or "proportion". The point is to describe the experience of architecture: how exactly does it contribute to the experience of a situation? For instance, the staging of an entrance situation, or the layout and visitor routes through a museum.From "context," through "guidance," "readability," "patina," "spatial structure," "symmetry" and "tectonics," to "width" (and "narrowness") or "window," the most important terms in architectural language are explained precisely and in detail. Wörterbuch der architektonischen Erfahrung - Wie wir Räume erleben Architektur wird erlebt - mit Intellekt und mit allen Sinnen, in der Bewegung und im Gebrauch. Doch um darüber tatsächlich zutreffend zu reden und zu urteilen, ist eine Klärung der Begriffe nötig, wenn die Schwammigkeit vermieden werden soll, die auf diesem Gebiet oft vorherrscht.Dieses Wörterbuch gibt ein Vokabular an die Hand, das ein Sprechen über Architektur jenseits der Erklärung konstruktiver Zusammenhänge oder der Beschreibung architektonischer Formen ermöglicht, unter der Verwendung geläufiger Begriffe wie "Dach", "Sockel", "Wand" und "Achse" oder "Proportion". Es geht darum, das Erleben von Architektur zu beschreiben: Wie trägt sie zum Erleben einer Situation bei? Etwa in der Inszenierung einer Eingangssituation oder mit der Wegeführung durch ein Museum.Von A bis Z, von "Ablesbarkeit" über "Fenster", "Kontext", "Orientierung", "Patina", "Raumgefüge", "Symmetrie" und "Tektonik" bis hin zu "Weite" (und "Enge") oder "Zentrum" werden die wichtigsten Begriffe der Architektursprache differenziert und vielschichtig erklärt.Präzise Handskizzen des Autors illustrieren den Text und bilden ein visuelles Gegengewicht zur Erläuterung von insgesamt 139 Stichworten.

Architectural design. --- Architecture -- Composition, proportion, etc. --- Architecture.

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In 1591, Giovanni Paolo Gallucci published his Della simmetria dei corpi humani, an Italian translation of Albrecht Dürer’s Four Books on Human Proporti on. While Dürer’s treatise had been translated earlier in the sixteenth-century into French and Latin, it was Gallucci’s Italian translation that endured in popularity as the most cited version of the text in later Baroque treatises, covering topics that were seen as central to arts education, connoisseurship, patronage, and the wider appreciation of the studia humanitati s in general. The text centres on the relationships between beauty and proportion, macrocosm and microcosm: relationships that were not only essential to the visual arts in the early modern era, but that cut across a range of disciplines – music, physiognomics and humoral readings, astronomy, astrology and cosmology, theology and philosophy, even mnemonics and poetry. In his version of the text, Gallucci expanded the educational potential of the treatise by adding a Preface, a Life of Dürer, and a Fifth Book providing a philosophical framework within which to interpret Dürer’s previous sections. This translation is the first to make these original contributions by Gallucci accessible to an English-speaking audience. Gallucci’s contributions illuminate the significance of symmetry and proportion in the contemporary education of the early modern era, informing our understanding of the intellectual history of this period, and the development of art theory and criticism. This is a valuable resource to early modern scholars and students alike, especially those specialising in history of art, philosophy, history of science, and poetry. As with all Open Book publications, this entire book is available to read for free on the publisher’s website. Printed and digital editions, together with supplementary digital material, can also be found at www.openbookpublishers.com

Arts & Humanities --- Medieval & Renaissance Studies --- Four Books on Human Proportion --- arts education --- beauty --- proportion