Handbook of Automated Reasoning

Chapter 11

Automated Reasoning in Geometry

Shang-Ching Chou; Xiao-Shan Gao

Contents

1  A history review of automated reasoning in geometry    709

2  Algebraic approaches to automated reasoning in geometry    712

2.1  Proving theorems in elementary geometries    712

2.2  Proving theorems involving inequalities    723

2.3  Proving theorems in differential geometry    728

2.4  Mechanical geometric formula derivation     730

3  Coordinate-free approaches to automated reasoning in geometry    732

3.1  Area method    732

3.2  Bracket algebra methods    733

3.3  Clifford algebra methods     734

3.4  Gröbner bases methods    734

4  AI approaches to automated reasoning in geometry    734

4.1  Gelernter's geometry machine  ...