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This paper presents a study, which is an extension of the research done by the first author on the elliptic paraboloid, and which is oriented to mathematics teaching to 17- to 19-year-olds architecture students. The first part presents a study of the graphic representation, modifications and apprehensions of the dynamic graphic register of the elliptic paraboloid when students interact with digital technology. The second part presents a device (sequence of tasks) that allows to the students articulating the apprehensions of the dynamic graphic register, as well as does the connection between mathematics, art and architecture, specifically in architectural constructions where these mathematical notions are present.

Mathematics Education Art and Architecture: Representations of the Elliptic Paraboloid