Study of Historical Geometric Problems by Means of CAS and DGS
AbstractCommon use of the computer algebra system wxMaxima and the dynamic mathematics software GeoGebra to solve several geometric problems on conics and loci from an 18th century textbook will be presented. In particular examples will be shown of how the use of these programs helped the authors to understand the method that our predecessors used to deal with the conic sections together with the solving the problems.
The combination of DGS and CAS has proved its worth to the authors in solving of such problems. DGS provides us with the dynamic construction and gives us an idea of the solution, e.g. a locus shape, whereas CAS helps us to find an equation and to prove or disprove the generality of a quality that is captured by the dynamic figure. The use of the computer changed the old problems, which to our students were originally solved in a rather strange way, into attractive modern problems. The authors will present the possible utilization of these problems in the teaching of mathematics and the benefits of doing so.