Geometrical Objects
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| Author | : Anthony Gerbino |
| Publisher | : Springer |
| Total Pages | : 326 |
| Release | : 2014-07-21 |
| Genre | : Architecture |
| ISBN | : 331905998X |
This volume explores the mathematical character of architectural practice in diverse pre- and early modern contexts. It takes an explicitly interdisciplinary approach, which unites scholarship in early modern architecture with recent work in the history of science, in particular, on the role of practice in the “scientific revolution”. As a contribution to architectural history, the volume contextualizes design and construction in terms of contemporary mathematical knowledge, attendant forms of mathematical practice, and relevant social distinctions between the mathematical professions. As a contribution to the history of science, the volume presents a series of micro-historical studies that highlight issues of process, materiality, and knowledge production in specific, situated, practical contexts. Our approach sees the designer’s studio, the stone-yard, the drawing floor, and construction site not merely as places where the architectural object takes shape, but where mathematical knowledge itself is deployed, exchanged, and amplified among various participants in the building process.
| Author | : Willard Van Orman Quine |
| Publisher | : MIT Press |
| Total Pages | : 309 |
| Release | : 2013-01-25 |
| Genre | : Philosophy |
| ISBN | : 0262518317 |
A new edition of Quine's most important work. Willard Van Orman Quine begins this influential work by declaring, "Language is a social art. In acquiring it we have to depend entirely on intersubjectively available cues as to what to say and when." As Patricia Smith Churchland notes in her foreword to this new edition, with Word and Object Quine challenged the tradition of conceptual analysis as a way of advancing knowledge. The book signaled twentieth-century philosophy's turn away from metaphysics and what Churchland calls the "phony precision" of conceptual analysis. In the course of his discussion of meaning and the linguistic mechanisms of objective reference, Quine considers the indeterminacy of translation, brings to light the anomalies and conflicts implicit in our language's referential apparatus, clarifies semantic problems connected with the imputation of existence, and marshals reasons for admitting or repudiating each of various categories of supposed objects. In addition to Churchland's foreword, this edition offers a new preface by Quine's student and colleague Dagfinn Follesdal that describes the never-realized plans for a second edition of Word and Object, in which Quine would offer a more unified treatment of the public nature of meaning, modalities, and propositional attitudes.
| Author | : Wolff-Michael Roth |
| Publisher | : Routledge |
| Total Pages | : 341 |
| Release | : 2011-05-09 |
| Genre | : Education |
| ISBN | : 1136732209 |
This study examines the origins of geometry in and out of the intuitively given everyday lifeworlds of children in a second-grade mathematics class. These lifeworlds, though pre-geometric, are not without model objects that denote and come to anchor geometric idealities that they will understand at later points in their lives. Roth's analyses explain how geometry, an objective science, arises anew from the pre-scientific but nevertheless methodic actions of children in a structured world always already shot through with significations. He presents a way of understanding knowing and learning in mathematics that differs from other current approaches, using case studies to demonstrate contradictions and incongruences of other theories – Immanuel Kant, Jean Piaget, and more recent forms of (radical, social) constructivism, embodiment theories, and enactivism – and to show how material phenomenology fused with phenomenological sociology provides answers to the problems that these other paradigms do not answer.
| Author | : Richard Lehrer |
| Publisher | : Routledge |
| Total Pages | : 519 |
| Release | : 2012-11-12 |
| Genre | : Education |
| ISBN | : 1136490515 |
This volume reflects an appreciation of the interactive roles of subject matter, teacher, student, and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the book is organized to highlight, first, the editors' vision of a general geometry education; second, the development of student thinking in everyday and classroom contexts; and third, the role of technologies. Rather than looking to high school geometry as the locus--and all too often, the apex--of geometric reasoning, the contributors to this volume suggest that reasoning about space can and should be successfully integrated with other forms of mathematics, starting at the elementary level and continuing through high school. Reintegrating spatial reasoning into the mathematical mainstream--indeed, placing it at the core of K-12 mathematics environments that promote learning with understanding--will mean increased attention to problems in modeling, structure, and design and reinvigoration of traditional topics such as measure, dimension, and form. Further, the editors' position is that the teaching of geometry and spatial visualization in school should not be compressed into a characterization of Greek geometry, but should include attention to contributions to the mathematics of space that developed subsequent to those of the Greeks. This volume is essential reading for those involved in mathematics education at all levels, including university faculty, researchers, and graduate students.
| Author | : Vladimir Balan |
| Publisher | : John Wiley & Sons |
| Total Pages | : 212 |
| Release | : 2011-09-23 |
| Genre | : Mathematics |
| ISBN | : 1118143760 |
Develops the theory of jet single-time Lagrange geometry and presents modern-day applications Jet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. With comprehensive chapters that outline topics ranging in complexity from basic to advanced, the book explores current and emerging applications across a broad range of fields, including mathematics, theoretical and atmospheric physics, economics, and theoretical biology. The authors begin by presenting basic theoretical concepts that serve as the foundation for understanding how and why the discussed theory works. Subusequent chapters compare the geometrical and physical aspects of jet relativistic time-dependent Lagrange geometry to the classical time-dependent Lagrange geometry. A collection of jet geometrical objects are also examined such as d-tensors, relativistic time-dependent semisprays, harmonic curves, and nonlinear connections. Numerous applications, including the gravitational theory developed by both the Berwald-Moór metric and the Chernov metric, are also presented. Throughout the book, the authors offer numerous examples that illustrate how the theory is put into practice, and they also present numerous applications in which the solutions of first-order ordinary differential equation systems are regarded as harmonic curves on 1-jet spaces. In addition, numerous opportunities are provided for readers to gain skill in applying jet single-time Lagrange geometry to solve a wide range of problems. Extensively classroom-tested to ensure an accessible presentation, Jet Single-Time Lagrange Geometry and Its Applications is an excellent book for courses on differential geometry, relativity theory, and mathematical models at the graduate level. The book also serves as an excellent reference for researchers, professionals, and academics in physics, biology, mathematics, and economics who would like to learn more about model-providing geometric structures.
| Author | : Lorenzo Magnani |
| Publisher | : Springer |
| Total Pages | : 1179 |
| Release | : 2017-05-22 |
| Genre | : Technology & Engineering |
| ISBN | : 3319305263 |
This handbook offers the first comprehensive reference guide to the interdisciplinary field of model-based reasoning. It highlights the role of models as mediators between theory and experimentation, and as educational devices, as well as their relevance in testing hypotheses and explanatory functions. The Springer Handbook merges philosophical, cognitive and epistemological perspectives on models with the more practical needs related to the application of this tool across various disciplines and practices. The result is a unique, reliable source of information that guides readers toward an understanding of different aspects of model-based science, such as the theoretical and cognitive nature of models, as well as their practical and logical aspects. The inferential role of models in hypothetical reasoning, abduction and creativity once they are constructed, adopted, and manipulated for different scientific and technological purposes is also discussed. Written by a group of internationally renowned experts in philosophy, the history of science, general epistemology, mathematics, cognitive and computer science, physics and life sciences, as well as engineering, architecture, and economics, this Handbook uses numerous diagrams, schemes and other visual representations to promote a better understanding of the concepts. This also makes it highly accessible to an audience of scholars and students with different scientific backgrounds. All in all, the Springer Handbook of Model-Based Science represents the definitive application-oriented reference guide to the interdisciplinary field of model-based reasoning.
| Author | : Giandomenico Sica |
| Publisher | : Polimetrica s.a.s. |
| Total Pages | : 270 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 8876990305 |
| Author | : Paolo Bussotti |
| Publisher | : Springer Nature |
| Total Pages | : 576 |
| Release | : |
| Genre | : |
| ISBN | : 3031542665 |
| Author | : Gabriele Galluzzo |
| Publisher | : BRILL |
| Total Pages | : 1401 |
| Release | : 2012-11-09 |
| Genre | : History |
| ISBN | : 9004235027 |
Focusing on the medieval reception of Book Zeta of Aristotle’s Metaphysics, Volume One of this work offers an unprecedented and philosophically oriented study of medieval ontology against the background of the current metaphysical debate on the nature of material objects. Volume Two makes available to scholars one of the culminating points in the medieval reception of Aristotle’s metaphysical thought by presenting the first critical edition of Book VII of Paul of Venice’s Commentary on Aristotle’s Metaphysics (1420-1424).
| Author | : Birgit Pepin |
| Publisher | : Springer Nature |
| Total Pages | : 1405 |
| Release | : |
| Genre | : |
| ISBN | : 303145667X |
