On the Unavoidable Uncertainty of Truth in Dynamic Geometry Proving

The aim of this note is to discuss some issues posed by the emergency of universal interfaces able to decide on the truth of geometric statements. More specifically, we consider a recent GeoGebra module allowing general users to verify standard geometric theorems. Working with this module in the con...

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Detalles Bibliográficos
Autores: Botana Ferreiro, Francisco Ramón|||0000-0002-0212-6470, Recio Muñiz, Tomás|||0000-0002-1011-295X
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/7266
Acceso en línea:http://hdl.handle.net/10902/7266
Access Level:acceso abierto
Palabra clave:Dynamic geometry
Automated theorem proving
GeoGebra
Varignon Theorem
Descripción
Sumario:The aim of this note is to discuss some issues posed by the emergency of universal interfaces able to decide on the truth of geometric statements. More specifically, we consider a recent GeoGebra module allowing general users to verify standard geometric theorems. Working with this module in the context of Varignon’s theorem, we were driven – by the characteristics of the GeoGebra interface– to perform a quite detailed study of the very diverse fate of attempting to automatically prove this statement, when using two different construction procedures.We highlight the relevance –for the theorem proving output– of expression power of the dynamic geometry interface, and we show that the algorithm deciding about the truth of some –even quite simple– statements can fall into a not true and not false situation, providing a source of confusion for a standard user and an interesting benchmark for geometers interested in discovering new geometric facts.