A trip under the eyes of a geometer

Abstract

This article presents a qualitative research of a theoretical nature, whose objective was to analyze the view of the forming geometer when making a trip, observing certain facts, objects, scenarios, etc. and associate them with mathematical content. Based on those observations and the collected records, we sought to visualize the extent to which specific Geometry content can be connected to others in Mathematic. Four incursions were made: the first connected the cusps of the Calculus with the facade of a building; the second visualized an atypical roof of a house in a conical shape; the third evoked Gauss and his Gaussian curvature in visualizing the lines resulting from the melting of Mount Aconcagua and, finally, the fourth compared the parable and the catenary in a portico to access a city. The established connections provide indicative of didactic possibilities of using Geometry for the formation of Mathematics teachers and are supported theoretically.

Keywords

• visualisation
• geometry
• cusp and catenary
• gaussian and average curvature
• mathematics education