Abstract: Publisher Summary This chapter reviews the methods developed for proving plane geometric theorems by examples. The main purpose of this survey is to provide researchers with an overview of the technique. In elementary plane geometry, diagrams or numerical examples are often used as counterexamples to disprove conjectures and used as intuitive models to find a rigorous proof of a theorem. However, experimental methods and inductive reasoning seem unacceptable in mathematics. A geometric statement without involving order relation may lead to several configurations involving order relations. It is shown how geometric theorem proving can be transformed into algebraic identity proving. Three methods to prove multivariate algebraic identities by example numerical verification are described. Two numerical algorithms for computing the dependency number of a polynomial on a normal ascending chain are also explained. It is found that for a geometric statement, each of the two algorithms embodies a method of proving by examples.
Publication Year: 2000
Publication Date: 2000-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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