Methods And Examples In Mechanical Geometry Theorem Proving
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| Author | : Shang-Ching Chou |
| Publisher | : World Scientific |
| Total Pages | : 490 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9789810215842 |
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.
| Author | : Wen-tsün Wu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 301 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 370916639X |
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.
| Author | : Daniel J. Velleman |
| Publisher | : Cambridge University Press |
| Total Pages | : 401 |
| Release | : 2006-01-16 |
| Genre | : Mathematics |
| ISBN | : 0521861241 |
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
| Author | : Leo Dorst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 479 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146120089X |
Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
| Author | : Ding-zhu Du |
| Publisher | : World Scientific |
| Total Pages | : 403 |
| Release | : 1992-09-14 |
| Genre | : Computers |
| ISBN | : 9814505609 |
This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.
| Author | : Ding-zhu Du |
| Publisher | : World Scientific |
| Total Pages | : 516 |
| Release | : 1995-01-25 |
| Genre | : Computers |
| ISBN | : 9814501638 |
This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm.
| Author | : Ding-Zhu Du |
| Publisher | : Springer |
| Total Pages | : 363 |
| Release | : 2019-08-01 |
| Genre | : Computers |
| ISBN | : 3030271951 |
This volume constitutes the proceedings of the 13th International Conference on Algorithmic Aspects in Information and Management, AAIM 2019, held in Bejing, China in August 2019. The 31 full papers presented were carefully reviewed and selected. The papers deal with most aspects of theoretical computer science and their applications. Special considerations are given to algorithmic research that is motivated by real-world applications.
| Author | : Amir Pnueli |
| Publisher | : World Scientific |
| Total Pages | : 322 |
| Release | : 1996-10-25 |
| Genre | : |
| ISBN | : 9814547360 |
This workshop brought together top researchers in logic and software engineering in the unique occasion of celebrating the 70th birthday of Professor C S Tang who has devoted much of his long research career to establishing a solid logic foundation for software engineering.
| Author | : Vladimir P. Gerdt |
| Publisher | : Springer |
| Total Pages | : 457 |
| Release | : 2013-08-15 |
| Genre | : Computers |
| ISBN | : 3319022970 |
This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
| Author | : W. W. Bledsoe |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 372 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : 082185027X |
