Abstract:

The purpose of this paper is to show how mathematics can relate the natural and man-made forms with equations and, conversely, how it allows the visualization of forms generated by equations.

We show how to take advantage, simultaneously, of 2D and 3D GeoGebra, to construct applications that simulate the generation of surfaces by families of generating functions. Regarding the curves to generate surfaces, a special attention is given to the conics to be studied using a 2D Geogebra application based on the general equation of conics.

Relations with art and architecture arise naturally. Works by renowned architects such as Antoni Gaudí, Felix Candela, Oscar Niemeyer and Santiago Calatrava are commented in terms of its forms and formulas.

We believe that the association of forms with formulas has great potential from an interactive point of view, providing an enrichment of knowledge and stimulating the development of activities in school environment.

Keywords:

Geometry, Geogebra, applications, architecture.