Machine Proofs In Geometry: Automated Production Of Readable Proofs For Geometry Theorems

Front Cover
World Scientific, Apr 6, 1994 - Mathematics - 480 pages
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.
 

Contents

Chapter 1 Geometry Preliminaries
1
Chapter 2 The Area Method
51
Chapter 3 Machine Proof in Plane Geometry
101
Chapter 4 Machine Proof in Solid Geometry
167
Chapter 5 Vectors and Machine Proofs
217
Chapter 6 Topics From Geometry
255
Bibliography
445
List of Symbols
455
Index
457
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