Automated Deduction in Geometry

This book constitutes the thoroughly refereed post-proceedings of the Third International Workshop on Automated Deduction in Geometry, ADG 2000, held in Zurich, Switzerland, in September 2000.The 16 revised full papers and two invited papers presented were carefully selected for publication during two rounds of reviewing and revision from a total of initially 31 submissions. Among the issues addressed are spatial constraint solving, automated proving of geometric inequalities, algebraic proof, semi-algebraic proofs, geometrical reasoning, computational synthetic geometry, incidence geometry, and nonstandard geometric proofs.

Inhalt

On Spatial Constraint Solving Approaches.- A Hybrid Method for Solving Geometric Constraint Problems.- Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study.- A Practical Program of Automated Proving for a Class of Geometric Inequalities.- Randomized Xero Testing of Radical Expressions and Elementary Geometry Theorem Proving.- Algebraic and Semialgebraic Proofs: Methods and Paradoxes.- Remarks on Geometric Theorem Proving.- The Kinds of Truth of Geometry Theorems.- A Complex Change of Variables for Geometrical Reasoning.- Reasoning about Surfaces Using Differential Zero and Ideal Decomposition.- Effective Methods in Computational Synthetic Geometry.- Decision Complexity in Dynamic Geometry.- Automated Theorem Proving in Incidence Geometry - A Bracket Algebra Based Elimination Method.- Qubit Logic, Algebra and Geometry.- Nonstandard Geometric Proofs.- Emphasizing Human Techniques in Automated Geometry Theorem Proving: A Practical Realization.- Higher-Order Intuitionistic Formalization and Proofs in Hilbert's Elementary Geometry.