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.
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