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Geometric Reasoning
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Book Synopsis Geometric Reasoning by : Deepak Kapur
Download or read book Geometric Reasoning written by Deepak Kapur and published by Bradford Book. This book was released on 1989 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry is at the core of understanding and reasoning about the form of physical objects and spatial relations which are now recognized to be crucial to many applications in artificial intelligence. The 20 contributions in this book discuss research in geometric reasoning and its applications to robot path planning, vision, and solid modeling. During the 1950s when the field of artificial intelligence was emerging, there were significant attempts to develop computer programs to mechanically perform geometric reasoning. This research activity soon stagnated because the classical AI approaches of rule based inference and heuristic search failed to produce impressive geometric, reasoning ability. The extensive research reported in this book, along with supplementary review articles, reflects a renaissance of interest in recent developments in algebraic approaches to geometric reasoning that can be used to automatically prove many difficult plane geometry theorems in a few seconds on a computer. Deepak Kapur is Professor in the Department of Computer Science at the State University of New York Albany. Joseph L. Mundy is a Coolidge Fellow at the Research and Development Center at General Electric. Geometric Reasoningis included in the series Special Issues from Artificial Intelligence: An International Journal. A Bradford Book
Book Synopsis Invariant Algebras and Geometric Reasoning by : Hongbo Li
Download or read book Invariant Algebras and Geometric Reasoning written by Hongbo Li and published by World Scientific. This book was released on 2008 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics OCo among them, GrassmannOCoCayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author and his collaborators' most recent, original development of GrassmannOCoCayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras OCo Cayley bracket algebra, conformal geometric algebra, and null bracket algebra OCo for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide. Sample Chapter(s). Chapter 1: Introduction (252 KB). Contents: Projective Space, Bracket Algebra and GrassmannOCoCayley Algebra; Projective Incidence Geometry with Cayley Bracket Algebra; Projective Conic Geometry with Bracket Algebra and Quadratic Grassmann-Cayley Algebra; Inner-product Bracket Algebra and Clifford Algebra; Geometric Algebra; Euclidean Geometry and Conformal GrassmannOCoCayley Algebra; Conformal Clifford Algebra and Classical Geometries. Readership: Graduate students in discrete and computational geometry, and computer mathematics; mathematicians and computer scientists.
Download or read book Taking Shape written by Joan Moss and published by . This book was released on 2016-04-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enrich Your Geometry Curriculum and Extend Your Students' Spatial Reasoning Research shows that children with good spatial skills perform better in mathematics overall. This research-based resource is a unique blend of professional learning and classroom activities. It includes: 32 field-tested and research-based activities designed to appeal to young children Guided lesson plans, including 15 videos, that serve as models for best practice in instruction Tips on observing, questioning, and assessing young children's geometric and spatial thinking Free access to website with videos, curriculum correlations, line masters, and observation guides
Book Synopsis Geometric Reasoning by : John Woodwark
Download or read book Geometric Reasoning written by John Woodwark and published by Oxford University Press, USA. This book was released on 1989 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: When computers are asked to deal with information about the shape of objects, the tasks required can be divided into those that can be attacked by algorithms and those that cannot. In computer graphics and image-processing, for example, despite great progress, it is really only the algorithmic processes that have been computerized. There are many more complex, less easily defined uses for shape information that elude solution. Geometric Reasoning deals with these activities. Its scope is broad, ranging beyond computational geometry or von Neumann architectures. Applications include shape modelling, computer graphics, image processing and computer vision.
Book Synopsis Handbook of Digital Resources in Mathematics Education by : Birgit Pepin
Download or read book Handbook of Digital Resources in Mathematics Education written by Birgit Pepin and published by Springer Nature. This book was released on with total page 1405 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Twenty-fourth Annual Conference of the Cognitive Science Society by : Wayne D. Gray
Download or read book Proceedings of the Twenty-fourth Annual Conference of the Cognitive Science Society written by Wayne D. Gray and published by Routledge. This book was released on 2019-04-24 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features the complete text of the material presented at the Twenty-Fourth Annual Conference of the Cognitive Science Society. As in previous years, the symposium included an interesting mixture of papers on many topics from researchers with diverse backgrounds and different goals, presenting a multifaceted view of cognitive science. The volume includes all papers, posters, and summaries of symposia presented at this leading conference that brings cognitive scientists together. The 2002 meeting dealt with issues of representing and modeling cognitive processes as they appeal to scholars in all subdisciplines that comprise cognitive science: psychology, computer science, neuroscience, linguistics, and philosophy.
Book Synopsis Developing Thinking in Geometry by : Sue Johnston-Wilder
Download or read book Developing Thinking in Geometry written by Sue Johnston-Wilder and published by Paul Chapman Educational Publishing. This book was released on 2005-09-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: "All readers can use this book to reignite their fascination with mathematics. Fosters not only a curiosity about geometry itself but crucially focuses on how learners can actively engage in thinking about geometry and its central key ideas."-Sylvia Johnson, Professor, Sheffield Hallam University"Exudes activity and interactivity. A book for learning geometry, learning to think more deeply about geometry, and also about its teaching and learning."-David Pimm, Professor, University of AlbertaDeveloping Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. Discussing key teaching principles, the book and its accompanying interactive CD-ROM include many activities encouraging readers to extend their own learning, and teaching practices.Drawing on innovative approaches for teaching and learning geometry developed by the Open University's Centre for Mathematics Education, this resource is constructed around the following key themes:InvarianceLanguage and points of viewReasoning using invarianceVisualizing and representing
Book Synopsis Spatial Information Theory by : Max J. Egenhofer
Download or read book Spatial Information Theory written by Max J. Egenhofer and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Spatial Information Theory, COSIT 2011, held in Belfast, ME, USA, in September 2011. The 23 revised full papers were carefully reviewed and selected from 55 submissions. They are organized in topical sections on maps and navigation, spatial change, spatial reasoning, spatial cognition and social aspects of space, perception and spatial semantics, and space and language.
Book Synopsis Researching and Using Progressions (Trajectories) in Mathematics Education by :
Download or read book Researching and Using Progressions (Trajectories) in Mathematics Education written by and published by BRILL. This book was released on 2019-02-04 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a contemporary focus on significant issues in STEM teaching, learning and research that are valuable in preparing students for a digital 21st century. The book chapters cover a wide spectrum of issues and topics using a wealth of research methodologies and methods.
Book Synopsis An Introduction to Geometric Reasoning in Four Settings by : Terrence Albert Lenahan
Download or read book An Introduction to Geometric Reasoning in Four Settings written by Terrence Albert Lenahan and published by Createspace Independent Publishing Platform. This book was released on 2016-09-23 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces the reasoning used to derive information about geometric objects. The development uses 3 basic steps and is repeated in 4 settings. First, the essential assumptions or axioms are identified from geometric activity like drawing on a page; next first-level properties are derived from the axioms; and finally 10 key theorems are proved based on the first two steps. Thus, inductive logic establishes a foundation and deductive logic hammers out the consequences. These steps are carried out for Plane, Solid, Spherical, and Hyperbolic Geometries. The first two Geometries, termed Euclidean, were initiated by Euclid almost 2400 years ago and added to by Euler, Monge, and others since then. The other two, termed non-Euclidean, have lines and figures confined to the surface of a sphere in Spherical Geometry and to a special hyperbolic plane in Hyperbolic Geometry. As a key difference of the non-Euclidean Geometries with Euclidean Geometry and with each other, there are no parallel lines in Spherical Geometry and there is a super-abundance of parallel lines in Hyperbolic Geometry. Looking at the same 10 theorems in 4 different settings provides a kind of controlled experiment that shows the effect of initial assumptions. After establishing basic properties of lines, angles, and circles in each setting, the book emphasizes triangles, or tetrahedra in Solid Geometry. Specific results include line and point concurrencies, the Pythagorean Theorem associated with each setting, areas and volumes, and properties of certain regular figures. The theory of similar triangles facilitates the proofs of several theorems in the Euclidean Geometries, but other means are required in the non-Euclidean ones. The final chapter illustrates how the previous approaches apply to trapezoids in Plane Geometry and their analogs in the other three settings. Over 100 figures, created from the Mathematica software system, help clarify the arguments used to verify results. Geometry is a gateway subject for those entering STEM fields, though the logic and rigor of the arguments has application to many fields. Also, geometry specifically calls for and fosters the ability to visualize situations and to represent them with figures, skills useful to designers of various products and enterprises. One indication that the study of geometry carries well beyond itself is the time Abraham Lincoln and Napoleon set aside to work on geometric questions. Napoleon even has a theorem named for him, which is part of the story here. A conclusion in the book, not usually noted, is that geometry is an experimental science. Questions that come up can be explored by drawing related figures to arrive at an answer or to test a conclusion. Accordingly, the reader is encouraged to approach this book with paper and pen at hand to test and explore. Working through the book in this way, the reader should acquire a thorough grounding in geometry and will have experience following, judging, and producing rigorous arguments, including some feeling for how to spot fallacies. With those skills, he or she will be well-equipped to go onto next steps, some of which are suggested at the end of the book.
Book Synopsis Intelligent CAD Systems III by : Paul J.W. ten Hagen
Download or read book Intelligent CAD Systems III written by Paul J.W. ten Hagen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of revised versions of papers presented at the Third Eurographics Workshop on Intelligent CAD Systems, which was held at Hotel Opduin on the island of Texel in The Netherlands, April 3-7, 1989. The workshop theme was Practical Experience and Evaluation. It included five paper presentation sessions, each followed by a discussion. The workshop closed with a general discussion. The book is therefore divided into five parts: design process, system architecture, languages, geometric reasoning, and user interface. A report on the discussion session, written by the session's moderator, concludes each part. These reports are not intended to be exact records of the discussion, but rather the moderators' summary of their contents. The aim of the workshop was to share the experience the participants gained by developing intelligent CAD (Computer Aided Design) systems, and to evaluate the developed systems to determine which features were still lacking. The workshop was organized as the last one in a series of three workshops under the same title. The first workshop focused on theoretical and methodological aspects, resulting in a sound theoretical basis for intelligent CAD systems. Implementational issues were discussed at the second workshop, paying attention to systems developed with reference to this basis. The experience and evaluation showed a dual outcome. Firstly, it resulted in the development of a new generation of intelligent CAD systems. Secondly, it led us to the development of new theories for intelligent CAD.
Book Synopsis Fundamentals of Digital Manufacturing Science by : Zude Zhou
Download or read book Fundamentals of Digital Manufacturing Science written by Zude Zhou and published by Springer Science & Business Media. This book was released on 2011-10-22 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The manufacturing industry will reap significant benefits from encouraging the development of digital manufacturing science and technology. Digital Manufacturing Science uses theorems, illustrations and tables to introduce the definition, theory architecture, main content, and key technologies of digital manufacturing science. Readers will be able to develop an in-depth understanding of the emergence and the development, the theoretical background, and the techniques and methods of digital manufacturing science. Furthermore, they will also be able to use the basic theories and key technologies described in Digital Manufacturing Science to solve practical engineering problems in modern manufacturing processes. Digital Manufacturing Science is aimed at advanced undergraduate and postgraduate students, academic researchers and researchers in the manufacturing industry. It allows readers to integrate the theories and technologies described with their own research works, and to propose new ideas and new methods to improve the theory and application of digital manufacturing science.
Author :Eduardo Bayro Corrochano Publisher :Springer Science & Business Media ISBN 13 :1461201594 Total Pages :607 pages Book Rating :4.4/5 (612 download)
Book Synopsis Geometric Algebra with Applications in Science and Engineering by : Eduardo Bayro Corrochano
Download or read book Geometric Algebra with Applications in Science and Engineering written by Eduardo Bayro Corrochano and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.
Book Synopsis Interdisciplinary Perspectives on Math Cognition by : Marcel Danesi
Download or read book Interdisciplinary Perspectives on Math Cognition written by Marcel Danesi and published by Springer Nature. This book was released on 2019-09-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.
Book Synopsis Teaching Primary Mathematics by : George Booker
Download or read book Teaching Primary Mathematics written by George Booker and published by Pearson Higher Education AU. This book was released on 2015-05-20 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifth edition of Teaching Primary Mathematics has been significantly revised and updated for the current educational environment. The organisation of the book has been redesigned to reflect feedback from readers and the approach taken by the Australian Curriculum: Mathematics. Teaching Primary Mathematics provides teachers and students with a sound framework for the successful teaching of mathematics to primary students. It is suitable both as a core text for primary student teachers and as an indispensable reference for practicing primary teachers seeking to update their knowledge.
Book Synopsis Advances in Materials Manufacturing Science & Technology XIII by : Dongming Guo
Download or read book Advances in Materials Manufacturing Science & Technology XIII written by Dongming Guo and published by Trans Tech Publications Ltd. This book was released on 2009-08-31 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume is part 2 of a mini-series on, Materials Manufacturing Science and Technology XII. It covers three topics: Modern design theory & methodology, MEMS & nanotechnology, Materials science & technology in manufacturing. Presented here is a collection of 125 papers selected from over 510 papers originally submitted by universities and industrial concerns all over the world. All of the papers have been peer-reviewed. The papers selected for this volume were chosen on the basis of their quality and their relevance to the topic. This work reflects the latest developments in this field; running the gamut from fundamentals to new techniques and applications.
Book Synopsis Beyond Shanghai and PISA by : Binyan Xu
Download or read book Beyond Shanghai and PISA written by Binyan Xu and published by Springer Nature. This book was released on 2021-05-07 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and measurable evaluation system in place to assess mathematical competency in China. While academic achievement surveys or evaluations are common, these can only give an overall conclusion about mathematical thinking skills or problem solving abilities. In response to this deficiency, China is beginning to carry out national projects that emphasize defining both a conceptual framework on core competencies in school mathematics and developing a corresponding assessment framework. Thus, the main focus of this volume is the current investigations of different mathematics competencies and mathematical disposition of Chinese students, with the aim of promoting interaction between domestic and international student performance assessment, to provide a more comprehensive understanding of mathematics competencies and disposition in mainland China, and to stimulate innovative new directions in research. The primary audience of this volume is the large group of researchers interested in mathematics competencies, mathematics teaching and learning in China, or comparative studies, or the relation of the three. The book will also appeal to teaching trainers or instructors, as well as be an appropriate resource for graduate courses or seminars at either the master’s or doctoral level.
