[PDF] Mechanical Theorem Proving In Riemann Geometry eBook

Author : University of Texas at Austin. Dept. of Computer Sciences
Publisher :
Page : 32 pages
File Size : 49,85 MB
Release : 1990
Category : Automatic theorem proving
ISBN :

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Abstract: "This paper studies the mechanical theorem proving in Riemann geometry using algebraic methods. We establish a theorem which can reduce a geometry statement in Riemann geometry to several substatements which are much easier to prove. For a class of constructive geometry statements, we present a method to generate sufficient non-degenerate conditions in geometric form mechanically. We also prove that an irreducible constructive statement is generally true if and only if it is universally true under the non-degenerate conditions generated by our method. More than 20 theorems other than those in projective geometry have been proved by our program."

Author : Wen-tsün Wu
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 45,74 MB
Release : 1994-04-14
Category : Computers
ISBN : 9783211825068

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This book is a translation of Professor Wu’s seminal Chinese book of 1984 on Automated Geometric Theorem Proving. The translation was done by his former student Dongming Wang jointly with Xiaofan Jin so that authenticity is guaranteed. Meanwhile, automated geometric theorem proving based on Wu’s method of characteristic sets has become one of the fundamental, practically successful, methods in this area that has drastically enhanced the scope of what is computationally tractable in automated theorem proving. This book is a source book for students and researchers who want to study both the intuitive first ideas behind the method and the formal details together with many examples.

Author : Wen-tsün Wu
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 17,86 MB
Release : 2012-12-06
Category : Computers
ISBN : 370916639X

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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 : Shang-Ching Chou
Publisher : World Scientific
Page : 490 pages
File Size : 23,53 MB
Release : 1994
Category : Mathematics
ISBN : 9789810215842

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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 : Leonor Godinho
Publisher : Springer
Page : 476 pages
File Size : 17,94 MB
Release : 2014-07-26
Category : Mathematics
ISBN : 3319086669

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Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Author : Dongming Wang
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 29,67 MB
Release : 1998-03-18
Category : Computers
ISBN : 9783540642978

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This book constitutes the thoroughly refereed and revised post-workshop proceedings of the International Workshop on Automated Deduction in Geometry, held in Toulouse, France, in September 1996. The revised extended papers accepted for inclusion in the volume were selected on the basis of double reviewing. Among the topics covered are automated geometric reasoning and the deduction applied to Dixon resultants, Gröbner bases, characteristic sets, computational geometry, algebraic geometry, and planet motion; furthermore the system REDLOG is demonstrated and the verification of geometric statements as well as the automated production of proof in Euclidean Geometry are present.