The Use of DGS and CAS in Proving Theorems


  • Pavel Pech University of Southern Bohemia, Czech Republic


The use of dynamic geometry systems (DGS) and computer algebra systems (CAS) changed teaching geometry at all school levels considerably. To solve a  problem students first visualize it by DGS then by changing parameters the problem is interactively modified and geometry properties like invariant points, lines, circles etc. are recognized. Using these knowledge a conjecture is stated and classically proved or disproved. But sometimes we do not have a  key idea to find a classical proof. Then the use of CAS can help. By the theory of automated geometry theorem proving we are able to prove many such theorems.  It turns out that integration of DGS and CAS is useful and helps to solve problems. This approach is demonstrated in a few examples of elementary geometry in a plane and space.






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