We tried that the choice made possible to approach concepts and mathematical procedures already studied, however, our teacher instigated us to deepen not only this knowledge, but also to contact with new mathematical subjects. In this sense, this work gave us the possibility to enrich ourselves culturally in a broader perspective. On the one hand, we became better acquainted with our historical and patrimonial legacy; on the other hand, we have approached mathematical questions that have given us the contact with different areas of Mathematics: geometry, algebra and probabilities. The contact with the history of Mathematics is also highlighted. In fact, it is particularly gratifying that, despite the doubts and difficulties experienced throughout the mathematical exploration of the defined itineraries, we learn Mathematics, but we also experience mathematical activity in another way, developing new ideas about the processes of this science.