The Exhaust Method and the use of Digital Technologies

Abstract

In this work we address the importance of understanding mathematical processes through history. We aim to present a proposal on how historical methods can be associated with Digital Technologies. To this end, we used the dynamic geometry software Geogebra to explore the exhaustion method developed by Eudoxus (408 - 355 BC) and refined by Archimedes (287 - 212 BC). Thus, we begin with a historical reference on the exhaustion method, then we present two constructions created in the Geogebra software that can be accessed via smartphone. By relating the exhaustion method to GeoGebra, we suggest that the combination of historical methods with Digital Technologies can provide a more practical and visual approach to teaching Mathematics, since direct manipulation of objects through dynamic geometry software can be a facilitator in the understanding and immediate analysis of the visualized constructions. Finally, in our considerations, we highlight the importance of balancing the use of Digital Technologies with a solid conceptual understanding, recognizing that easy access to digital tools should not compromise the deep understanding of mathematical foundations, and emphasizing that the intersection between history and the modern can improve the understanding of Mathematics in response to technological innovations.