In this article, we discuss how Geometry can be constituted and some of its different forms of representation. To achieve this, we present historical and conceptual aspects seeking to address how mathematical objects are treated from three different perspectives: Euclidean, Spherical, and Origami Geometry. We argue that Geometry is constantly developing and, therefore, it is important to debate these issues in Mathematics Education. To this end, we will focus on possibilities to discuss the axioms through manipulable objects and technologies, aiming to contribute to the classroom and promote the breaking of a fragmented view of knowledge.