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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.
This volume completes the English adaptation of a classical Russian textbook in elementary Euclidean geometry. The 1st volume subtitled "Book I. Planimetry" was published in 2006 (ISBN 0977985202). This 2nd volume (Book II. Stereometry) covers solid geometry, and contains a chapter on vectors, foundations, and introduction in non-Euclidean geometry added by the translator. The book intended for high-school and college students, and their teachers. Includes 317 exercises, index, and bibliography.
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.
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.
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.
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.
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.
An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.
Handbook of Automated Reasoning
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.