Dynamic Investigation of Area Conservation Properties Using Computer Technology in a Classroom Activity

Abstract

The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs. Some of the examples are original, and all are beautiful and insightful. The mathematical proofs of the selected examples are very simple and do not require the use of any "heavy" mathematical tools. All the examples have links to applets prepared in GeoGebra-Tube. The consequences of all the examples can be formulized as mathematical propositions, and vice versa, meaning any mathematical proposition might demonstrate a situation of variance and invariance properties.