Geometry Intuition And Concepts
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Geometry Intuition And Concepts
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Author : Jost-Hinrich Eschenburg
language : en
Publisher: Springer Nature
Release Date : 2022-10-31
Geometry Intuition And Concepts written by Jost-Hinrich Eschenburg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-31 with Mathematics categories.
This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
The Geometry Of Schemes
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
The Geometry Of Schemes written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Geometry Intuition And Concepts
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Author : Jost-Hinrich Eschenburg
language : en
Publisher:
Release Date : 2022
Geometry Intuition And Concepts written by Jost-Hinrich Eschenburg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
This book deals with the geometry of the visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes. Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is the content of this book. This is intended to close an often-lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, it justifies descriptive geometric argumentation, because its embedding in the strict mathematical language is clarified. Geometric terms are of very different kinds; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, some require angles and distances, and others symmetry. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the one last-mentioned "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. This book is a translation of the original German 1st edition Geometrie - Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
A Primer Of Infinitesimal Analysis
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Author : John L. Bell
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-07
A Primer Of Infinitesimal Analysis written by John L. Bell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-07 with Mathematics categories.
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Geometry Intuition And Concepts
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Author : Jost-Hinrich Eschenburg
language : en
Publisher:
Release Date : 2022
Geometry Intuition And Concepts written by Jost-Hinrich Eschenburg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Electronic books categories.
This book deals with the geometry of the visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes. Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is the content of this book. This is intended to close an often-lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, it justifies descriptive geometric argumentation, because its embedding in the strict mathematical language is clarified. Geometric terms are of very different kinds; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, some require angles and distances, and others symmetry. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the one last-mentioned "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. This book is a translation of the original German 1st edition Geometrie -- Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Space Geometry And Kant S Transcendental Deduction Of The Categories
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Author : Thomas C. Vinci
language : en
Publisher:
Release Date : 2015
Space Geometry And Kant S Transcendental Deduction Of The Categories written by Thomas C. Vinci and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Philosophy categories.
Thomas C. Vinci aims to reveal and assess the structure of Kant's argument in the Critique of Pure Reason called the "Transcendental Deduction of the Categories." At the end of the first part of the Deduction in the B-edition Kant states that his purpose is achieved: to show that all intuitions in general are subject to the categories. On the standard reading, this means that all of our mental representations, including those originating in sense-experience, are structured by conceptualization. But this reading encounters an exegetical problem: Kant states in the second part of the Deduction that a major part of what remains to be shown is that empirical intuitions are subject to the categories. How can this be if it has already been shown that intuitions in general are subject to the categories? Vinci calls this the Triviality Problem, and he argues that solving it requires denying the standard reading. In its place he proposes that intuitions in general and empirical intuitions constitute disjoint classes and that, while all intuitions for Kant are unified, there are two kinds of unification: logical unification vs. aesthetic unification. Only the former is due to the categories. A second major theme of the book is that Kant's Idealism comes in two versions-for laws of nature and for objects of empirical intuition-and that demonstrating these versions is the ultimate goal of the Deduction of the Categories and the similarly structured Deduction of the Concepts of Space, respectively. Vinci shows that the Deductions have the argument structure of an inference to the best explanation for correlated domains of explananda, each arrived at by independent applications of Kantian epistemic and geometrical methods.
Geometry And Topological Concepts
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Author : Dr. P. Somashekhara
language : en
Publisher: RK Publication
Release Date : 2024-09-21
Geometry And Topological Concepts written by Dr. P. Somashekhara and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-21 with Juvenile Nonfiction categories.
Geometry and Topological Concepts is an exploration of the fundamental principles and applications of geometry and topology in mathematics and related fields. This book delves into the intricacies of shapes, sizes, and the properties of space, emphasizing the connections between these areas of study. It covers essential topics such as Euclidean and non-Euclidean geometries, topological spaces, and geometric transformations, providing readers with both theoretical foundations and practical examples. Ideal for students and professionals, it fosters a deeper understanding of the mathematical structures that underpin our world.
New Foundations For Physical Geometry
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Author : Tim Maudlin
language : en
Publisher:
Release Date : 2014-02
New Foundations For Physical Geometry written by Tim Maudlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02 with Mathematics categories.
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Philosophy And Geometry
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Author : L. Magnani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Philosophy And Geometry written by L. Magnani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.
Fundamental Concepts Of Geometry
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Author : Bruce E. Meserve
language : en
Publisher: Courier Corporation
Release Date : 2014-12-08
Fundamental Concepts Of Geometry written by Bruce E. Meserve and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-08 with Mathematics categories.
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.