A Simple Geometric Theorem with a Construsction Configuration Whose Truthfulness Depends on the Base Field Considered

Abstract

It is well-known that the truthfulness of some theorns in plane geometry depends on the base field considered. We shall show a a simple example of geometric theorem, whose corresponding geometric configuration in the real case, that is always true in the real case and that is "almost always" false in the complex case (more precisely variety). We believe this is an eye-catching example illustrating how the results from exploration carried out with a Dynamic Geometry System or from computation carried out using a Coumputer Algebra System should be carefully analyzed.