Machine Proofs In Geometry
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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 | : A. I. Fetisov |
Publisher | : Courier Corporation |
Total Pages | : 130 |
Release | : 2012-06-11 |
Genre | : Mathematics |
ISBN | : 0486154920 |
This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Author | : Martin Aigner |
Publisher | : Springer Science & Business Media |
Total Pages | : 194 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662223430 |
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author | : Richard H. Hammack |
Publisher | : |
Total Pages | : 314 |
Release | : 2016-01-01 |
Genre | : Mathematics |
ISBN | : 9780989472111 |
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author | : Martin Aigner |
Publisher | : Springer Science & Business Media |
Total Pages | : 234 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662054124 |
The mathematical heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background.
Author | : Ding-Zhu Du |
Publisher | : World Scientific |
Total Pages | : 520 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9789810218768 |
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 | : Dingzhu Du |
Publisher | : World Scientific |
Total Pages | : 414 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9789810209667 |
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 | : Serge Lang |
Publisher | : |
Total Pages | : 475 |
Release | : 1988-01 |
Genre | : Mathematics |
ISBN | : 9783540967873 |
Author | : Chris McMullen |
Publisher | : |
Total Pages | : 206 |
Release | : 2019-05-24 |
Genre | : |
ISBN | : 9781941691502 |
This geometry workbook includes: 64 proofs with full solutions, 9 examples to help serve as a guide, and a review of terminology, notation, and concepts. A variety of word topics are covered, including: similar and congruent triangles, the Pythagorean theorem, circles, chords, tangents, alternate interior angles, the triangle inequality, the angle sum theorem, quadrilaterals, regular polygons, area of plane figures, inscribed and circumscribed figures, and the centroid of a triangle. The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook to share his strategies for writing geometry proofs.
Author | : Pascal Schreck |
Publisher | : Springer |
Total Pages | : 268 |
Release | : 2011-11-10 |
Genre | : Computers |
ISBN | : 364225070X |
This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on Automated Deduction in Geometry, ADG 2010, held in Munich, Germany in July 2010. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement from the lectures given at the workshop. Topics addressed by the papers are incidence geometry using some kind of combinatoric argument; computer algebra; software implementation; as well as logic and proof assistants.