Mechanical Theorem Proving In Geometries

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Mechanical Theorem Proving In Geometries

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Author : Wen-tsün Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mechanical Theorem Proving In Geometries written by Wen-tsün Wu 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 Computers categories.

There seems to be no doubt that geometry originates from such practical activ ities as weather observation and terrain survey. But there are different manners, methods, and ways to raise the various experiences to the level of theory so that they finally constitute a science. F. Engels said, "The objective of mathematics is the study of space forms and quantitative relations of the real world. " Dur ing the time of the ancient Greeks, there were two different methods dealing with geometry: one, represented by the Euclid's "Elements," purely pursued the logical relations among geometric entities, excluding completely the quantita tive relations, as to establish the axiom system of geometry. This method has become a model of deduction methods in mathematics. The other, represented by the relevant work of Archimedes, focused on the study of quantitative re lations of geometric objects as well as their measures such as the ratio of the circumference of a circle to its diameter and the area of a spherical surface and of a parabolic sector. Though these approaches vary in style, have their own features, and reflect different viewpoints in the development of geometry, both have made great contributions to the development of mathematics. The development of geometry in China was all along concerned with quanti tative relations.

Mechanical Geometry Theorem Proving

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Author : Shang-Ching Chou
language : en
Publisher: Springer
Release Date : 1988

Mechanical Geometry Theorem Proving written by Shang-Ching Chou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Computers categories.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Machine Proofs In Geometry

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Author : Shang-Ching Chou
language : en
Publisher: World Scientific
Release Date : 1994

Machine Proofs In Geometry written by Shang-Ching Chou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.

Mechanical Theorem Proving In Geometries

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Author : Wen-tsun Wu
language : en
Publisher:
Release Date : 1994-04-14

Mechanical Theorem Proving In Geometries written by Wen-tsun Wu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-14 with categories.

Elimination Practice

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Author : Dongming Wang
language : en
Publisher: World Scientific
Release Date : 2004

Elimination Practice written by Dongming Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.

Polynomial Elimination at Work; The Epsilon Library; The CharSets Package; The TriSys and SiSys Modules; The GEOTHER Environment; Relevant Elimination Tools; Solving Polynomial Systems; Automated Theorem Proving and Discovering in Geometry; Symbolic Geometric Computation; Selected Problems in Computer Mathematics.

10th International Conference On Automated Deduction

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Author : Mark E. Stickel
language : en
Publisher: Springer Science & Business Media
Release Date : 1990

10th International Conference On Automated Deduction written by Mark E. Stickel 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 1990 with Artificial intelligence categories.

"This volume contains the papers presented at the 10th International Conference on Automated Deduction (CADE-10). CADE is the major forum at which research on all aspects of automated deduction is presented. Although automated deduction research is also presented at more general artificial intelligence conferences, the CADE conferences have no peer in the concentration and quality of their contributions to this topic. The papers included range from theory to implementation and experimentation, from propositional to higher-order calculi and nonclassical logics; they refine and use a wealth of methods including resolution, paramodulation, rewriting, completion, unification and induction; and they work with a variety of applications including program verification, logic programming, deductive databases, and theorem proving in many domains. The volume also contains abstracts of 20 implementations of automated deduction systems. The authors of about half the papers are from the United States, many are from Western Europe, and many too are from the rest of the world. The proceedings of the 5th, 6th, 7th, 8th and 9th CADE conferences are published as Volumes 87, 138, 170, 230, 310 in the series Lecture Notes in Computer Science."--PUBLISHER'S WEBSITE.

Handbook Of Geometric Constraint Systems Principles

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Author : Meera Sitharam
language : en
Publisher: CRC Press
Release Date : 2018-07-20

Handbook Of Geometric Constraint Systems Principles written by Meera Sitharam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-20 with Mathematics categories.

The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.

Automated Deduction Cade 12

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Author : Alan Bundy
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-06-08

Automated Deduction Cade 12 written by Alan Bundy 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 1994-06-08 with Computers categories.

This volume contains the reviewed papers presented at the 12th International Conference on Automated Deduction (CADE-12) held at Nancy, France in June/July 1994. The 67 papers presented were selected from 177 submissions and document many of the most important research results in automated deduction since CADE-11 was held in June 1992. The volume is organized in chapters on heuristics, resolution systems, induction, controlling resolutions, ATP problems, unification, LP applications, special-purpose provers, rewrite rule termination, ATP efficiency, AC unification, higher-order theorem proving, natural systems, problem sets, and system descriptions.

Automated Deduction In Geometry

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Author : Franz Winkler
language : en
Publisher: Springer
Release Date : 2004-05-06

Automated Deduction In Geometry written by Franz Winkler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-06 with Mathematics categories.

This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Automated Deduction in Geometry, ADG 2002, held at Hagenberg Castle, Austria in September 2002. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement. Among the issues addressed are theoretical and methodological topics, such as the resolution of singularities, algebraic geometry and computer algebra; various geometric theorem proving systems are explored; and applications of automated deduction in geometry are demonstrated in fields like computer-aided design and robotics.

Handbook Of Automated Reasoning

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Author : Alan J.A. Robinson
language : en
Publisher: Gulf Professional Publishing
Release Date : 2001-06-21

Handbook Of Automated Reasoning written by Alan J.A. Robinson and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-21 with Computers categories.

Handbook of Automated Reasoning.