Machine Proofs In Geometry: Automated Production Of Readable Proofs For Geometry TheoremsThis 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
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 |
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Common terms and phrases
A₁ ABē ACē affine geometry algebraic Algorithm altitude angle area method Axiom B₁ B₂ bisector C₁ centroid Ceva's theorem circumcenter O A B C circumcircle co-side theorem Constructive description circle Constructive description points cyclic quadrilateral D₁ description points A B C eliminate points exterior products Figure foot D A B C formula full-angles geometry quantities geometry statement geometry theorems inter C₁ inter F Lemma line passing line PQ LINE U V lratio M₁ M₂ machine proof midpoint ndg condition O₁ orthic triangle orthocenter P₁ PABA PABC PACA PACB parallel parallelogram PBAC PBCB perpendicular plane polynomial Proposition Pythagoras difference quadrilateral r₁ S. C. Chou SABA SABC SABCD SABD SABO SABP SACA SACD SACE SADE SARC SBCD SBCE Show simplify 1 Example Souv SPQR Take a point Theorem Proving three points triangle ABC VABCD vector vector space