Selected Topics In Geometry With Classical Vs. Computer Proving

This textbook presents various automatic techniques based on Gröbner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects which cannot be easily done with a ruler and compass.

Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically without using computer where possible so that readers can compare the strengths and weaknesses of both approaches.

Contents: Automatic Theorem Proving; Generalization of the Formula of Heron; Simson Wallace Theorem; Transversals in a Polygon; Petr Douglas Neumann's Theorem; Geometric Inequalities; Regular Polygons.