Geometric Reasoning

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Geometric Reasoning

Author : Deepak Kapur
Publisher : Bradford Book
ISBN 13 :
Total Pages : 524 pages
Book Rating : 4.:/5 (321 download)

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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

Invariant Algebras and Geometric Reasoning

Author : Hongbo Li
Publisher : World Scientific
ISBN 13 : 9812770119
Total Pages : 533 pages
Book Rating : 4.8/5 (127 download)

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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.

Fostering Geometric Thinking

Author : Mark Driscoll
Publisher : Heinemann Educational Books
ISBN 13 : 9780325093130
Total Pages : 144 pages
Book Rating : 4.0/5 (931 download)

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Book Synopsis Fostering Geometric Thinking by : Mark Driscoll

Download or read book Fostering Geometric Thinking written by Mark Driscoll and published by Heinemann Educational Books. This book was released on 2017-05-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Trends in International Mathematics and Science Study has shown that American schools have consistently helped students understand algebraic and statistical concepts, leading to high achievement internationally. Now it's time to do the same for geometry. Mark Driscoll, author of the powerful and popular Fostering Algebraic Thinking, takes up the challenge and leads you to new, research-based ways to improve how your students conceptualize and apply geometric ideas. With Fostering Geometric Thinking any math teacher can discover essential, practical ideas for helping students cultivate geometric habits of mind that lead to success in this crucial mathematical subject. The book focuses on rigorous, problem-based teaching that encourages students to deepen their thinking in three key geometric strands: geometric properties geometric transformations measurement of geometric objects. Fostering Geometric Thinking shows you how the interplay of these strands helps students devise multiple solutions and develop a broader sense of geometric principles. It's loaded with helpful resources, including: engaging problems to use in your classroom examples of student solutions to these problems transcripts of classroom interactions online resources featuring in-the-field footage of students working through open-ended problems highlighted in the book. Geometry is a vital component of mathematical understanding, and it's time that it received the same attention that algebra and statistics do. With engaging problems and straightforward suggestions that can help students deepen, recognize, and describe their thinking, Fostering Geometric Thinking is the resource you need to ensure that when it comes to geometry, your students know all the angles.

Geometric Reasoning

Author : John Woodwark
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.3/5 (91 download)

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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.

Developing Thinking in Geometry

Author : Sue Johnston-Wilder
Publisher : Paul Chapman Educational Publishing
ISBN 13 : 9781412911696
Total Pages : 300 pages
Book Rating : 4.9/5 (116 download)

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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

Developing Thinking in Algebra

Author : John Mason
Publisher : Paul Chapman Educational Publishing
ISBN 13 : 9781412911719
Total Pages : 342 pages
Book Rating : 4.9/5 (117 download)

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Book Synopsis Developing Thinking in Algebra by : John Mason

Download or read book Developing Thinking in Algebra written by John Mason and published by Paul Chapman Educational Publishing. This book was released on 2005-04-23 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Mason, Graham, and Johnston-Wilder have admirably succeeded in casting most of school algebra in terms of generalisation activity? not just the typical numerical and geometric pattern-based work, but also solving quadratics and simultaneous equations, graphing equations, and factoring. The authors raise our awareness of the scope of generalization and of the power of using this as a lens not just for algebra but for all of mathematics!' - Professor Carolyn Kieran, Departement de Mathematiques, Universite du Quebec a Montreal Algebra has always been a watershed for pupils learning mathematics. This book will enable you to think about yourself as a learner of algebra in a new way, and thus to teach algebra more successfully, overcoming difficulties and building upon skills that all learners have. This book is based on teaching principles developed by the team at The Open University's Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning algebra. Written for teachers working with pupils aged 7-16, it includes numerous tasks ready for adaption for your teaching and discusses principles that teachers have found useful in preparing and conducting lessons. This is a 'must have' resource for all teachers of mathematics, primary or secondary, and their support staff. Anyone who wishes to create an understanding and enthusiasm for algebra, based upon firm research and effective practice, will enjoy this book. This book is the course reader for The Open University Course ME625 Developing Algebraic Thinking

Proceedings of the Twenty-fourth Annual Conference of the Cognitive Science Society

Author : Wayne D. Gray
Publisher : Routledge
ISBN 13 : 1317708326
Total Pages : 312 pages
Book Rating : 4.3/5 (177 download)

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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.

Spatial Information Theory

Author : Max J. Egenhofer
Publisher : Springer Science & Business Media
ISBN 13 : 3642231950
Total Pages : 465 pages
Book Rating : 4.6/5 (422 download)

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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.

Researching and Using Progressions (Trajectories) in Mathematics Education

Author :
Publisher : BRILL
ISBN 13 : 9004396446
Total Pages : 255 pages
Book Rating : 4.0/5 (43 download)

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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: The relationship between research and practice has long been an area of interest for researchers, policy makers, and practitioners alike. One obvious arena where mathematics education research can contribute to practice is the design and implementation of school mathematics curricula. This observation holds whether we are talking about curriculum as a set of broad, measurable competencies (i.e., standards) or as a comprehensive set of resources for teaching and learning mathematics. Impacting practice in this way requires fine-grained research that is focused on individual student learning trajectories and intimate analyses of classroom pedagogical practices as well as large-scale research that explores how student populations typically engage with the big ideas of mathematics over time. Both types of research provide an empirical basis for identifying what aspects of mathematics are important and how they develop over time. This book has its origins in independent but parallel work in Australia and the United States over the last 10 to 15 years. It was prompted by a research seminar at the 2017 PME Conference in Singapore that brought the contributors to this volume together to consider the development and use of evidence-based learning progressions/trajectories in mathematics education, their basis in theory, their focus and scale, and the methods used to identify and validate them. In this volume they elaborate on their work to consider what is meant by learning progressions/trajectories and explore a range of issues associated with their development, implementation, evaluation, and on-going review. Implications for curriculum design and future research in this field are also considered. Contributors are: Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates, Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne Siemon, Max Stephens, Ron Tzur, and Jane Watson.

Intelligent CAD Systems III

Author : Paul J.W. ten Hagen
Publisher : Springer Science & Business Media
ISBN 13 : 3642843921
Total Pages : 268 pages
Book Rating : 4.6/5 (428 download)

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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.

Taking Shape

Author : Joan Moss
Publisher :
ISBN 13 : 9780134153490
Total Pages : 272 pages
Book Rating : 4.1/5 (534 download)

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Book Synopsis Taking Shape by : Joan Moss

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

Fundamentals of Digital Manufacturing Science

Author : Zude Zhou
Publisher : Springer Science & Business Media
ISBN 13 : 0857295640
Total Pages : 373 pages
Book Rating : 4.8/5 (572 download)

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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.

Geometric Algebra with Applications in Science and Engineering

Author : Eduardo Bayro Corrochano
Publisher : Springer Science & Business Media
ISBN 13 : 1461201594
Total Pages : 607 pages
Book Rating : 4.4/5 (612 download)

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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.

Teaching Primary Mathematics

Author : George Booker
Publisher : Pearson Higher Education AU
ISBN 13 : 1486004881
Total Pages : 593 pages
Book Rating : 4.4/5 (86 download)

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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.

Interdisciplinary Perspectives on Math Cognition

Author : Marcel Danesi
Publisher : Springer Nature
ISBN 13 : 3030225372
Total Pages : 343 pages
Book Rating : 4.0/5 (32 download)

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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 343 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.

Advances in Materials Manufacturing Science & Technology XIII Volume II

Author : Dongming Guo
Publisher : Trans Tech Publications Ltd
ISBN 13 : 3038132489
Total Pages : 755 pages
Book Rating : 4.0/5 (381 download)

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Book Synopsis Advances in Materials Manufacturing Science & Technology XIII Volume II by : Dongming Guo

Download or read book Advances in Materials Manufacturing Science & Technology XIII Volume II written by Dongming Guo and published by Trans Tech Publications Ltd. This book was released on 2009-08-31 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Design Theory and Methodology, MEMS & Nanotechnology, Material Science & Technology in Manufacturing Advanced Manufacturing Technology, Equipment and Manufacturing Systems & Automation Proceedings: Selected, peer reviewed papers from the 13th International Manufacturing Conference in China, September 21-23, 2009, Dalian, China

Beyond Shanghai and PISA

Author : Binyan Xu
Publisher : Springer Nature
ISBN 13 : 3030681572
Total Pages : 364 pages
Book Rating : 4.0/5 (36 download)

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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.