## Automated Deduction in Geometry: Second International Workshop, ADG'98, Beijing, China, August 1-3, 1998, ProceedingsXiao-Shan Gao, Dongming Wang, Lu Yang The Second International Workshop on Automated Deduction in Geometry (ADG ’98) was held in Beijing, China, August 1–3, 1998. An increase of interest in ADG ’98 over the previous workshop ADG ’96 is represented by the notable number of more than 40 participants from ten countries and the strong tech- cal program of 25 presentations, of which two one-hour invited talks were given by Professors Wen-tsun ̈ Wu and Jing-Zhong Zhang. The workshop provided the participants with a well-focused forum for e?ective exchange of new ideas and timely report of research progress. Insight surveys, algorithmic developments, and applications in CAGD/CAD and computer vision presented by active - searchers, together with geometry software demos, shed light on the features of this second workshop. ADG ’98 was hosted by the Mathematics Mechanization Research Center (MMRC) with ?nancial support from the Chinese Academy of Sciences and the French National Center for Scienti?c Research (CNRS), and was organized by the three co-editors of this proceedings volume. The papers contained in the volume were selected, under a strict refereeing procedure, from those presented at ADG ’98 and submitted afterwards. Most of the 14 accepted papers were carefully revised and some of the revised versions were checked again by external reviewers. We hope that these papers cover some of the most recent and signi?cant research results and developments and re?ect the current state-of-the-art of ADG. |

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### Contents

Automatic Geometry TheoremProving and Automatic Geometry ProblemSolving | 1 |

Solving Geometric Problems with Real Quantifier Elimination | 14 |

Automated Discovering and Proving for Geometric Inequalities | 30 |

Proving Newtons Propositio Kepleriana Using Geometry and Nonstandard Analysis in Isabelle | 47 |

Readable Machine Solving in Geometry and ICAI Software MSG | 67 |

Plane Euclidean Reasoning | 86 |

A Clifford Algebraic Method for Geometric Reasoning | 111 |

Clifford Term Rewriting for Geometric Reasoning in 3D | 130 |

Some Applications of Clifford Algebra to Geometries | 156 |

Decomposing Algebraic Varieties | 180 |

An Application of Automatic Theorem Proving in Computer Vision | 207 |

Automated Geometry Diagram Construction and Engineering Geometry | 232 |

A 2D Geometric Constraint Solver for Parametric Design Using Graph Analysis and Reduction | 258 |

Variant Geometry Analysis and Synthesis in Mechanical CAD | 275 |

286 | |

### Other editions - View all

Automated Deduction in Geometry: Second International Workshop, ADG'98 ... Xiao-Shan Gao,Dongming Wang,Lu Yang No preview available - 1999 |

Automated Deduction in Geometry: Second International Workshop, ADG'98 ... Xiao-Shan Gao,Dongming Wang,Lu Yang No preview available - 1999 |

### Common terms and phrases

algebraic variety algorithm angle application approach atomic formulas Automated Reasoning basic basis called characteristic set Chou Clifford algebra Clifford algebraic polynomial cluster complex numbers computer vision configuration construction cylindrical algebraic decomposition deﬁne defined denoted diagram distinct real dual quaternions ellipse Enneper surface equivalent Euclidean Euclidean geometry example finite full-angles geometric constraint geometric entities geometric objects Geometric Reasoning geometry problems geometry theorem proving gr(t graph Gröbner bases intersection irreducible Lemma len(C len(E len(P len(Q linear linkage mechanism LNAI Mathematics Mechanical method multivector Newton’s normal form obtained outer product parameters plane polset polynomial equations polynomial set Proc procedure proof quantifier elimination r-blade ratio readable real numbers real solution(s redlog represented result ruler-and-compass rules sat(T scalar Section separable entity group simplifier solutions solving Springer-Verlag SRules step symbolic techniques transformation triangle triangular set variant vector Wachter model Wang zero decomposition Zero(P Zhang