Formas & Fórmulas

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Formas & Fórmulas at the hall of the Sciences faculty of University of Lisbon.

Formas & Fórmulas (Shapes and Formulas) is a Portuguese exhibition conceived in 2012 for the Museu Nacional de História Natural e da Ciência in Lisbon, Portugal. It was on display at the museum from June 1, 2012, to July 15, 2016. Since October 24, 2016, it is displayed at the hall of the Science Faculty (building C6) of the Universidade de Lisboa.


The modules of the exhibition include images, 3D-printed sculptures, hands-on exibit, historical and reproductions of mathematical models, films and computer stations with software. The exhibition is organized in four sections.

Lines and revolutions

Hands-on exhibits for Lines and revolutions.

This section presents panels about conics, quadrics and surfaces of revolution. Some hands-on exhibits allow to experience ruled surfaces and reflective properties of conics.

Surfaces and constructions

This section explores mathematics in architecture. It compares for instance the catenary arches with parablolas in hanging bridges, and shows the use of geometric shapes in modern architecture (by O. Niemeyer, A. Gaudí, S. Calatrava, F. Candela...) Exhibits include scale models, images, and the film "Superfícies Curvas"

Surfaces and complications

Here the exhibition deepens into pure mathematics, going beyond quadratic equations and elementary curves. The main topic are algebraic surfaces, exploring topics as surfaces with many singularities, surfaces containing straight lines, or a remarkable collection of the 45 non-ruled cubics as 3D sculptures. Exhibits on this include 3D printed models of surfaces, 3D sculptures in plexiglass cubes, historical string and plaster models, an interactive station with the program SURFER, and an art gallery of images of surfaces.

The 45 non-ruled cubics.

Images and visualizations

In addition to the algebraic surfaces, other visualizations of mathematical ideas are also in the exhibition. A collecion of 3D printed sculptures represent the possible geometries for 2-manifolds and 3-manifolds. Symmetries or cryptography can be explored with software and videos.

The exhibition also includes several programs and films from the initiative Mathematics of Planet Earth 2013.

See also