Class Three-dimensionality

The Tridimensionality Course Unit focuses on understanding and experimenting with the transition from two-dimensional to three-dimensional. This passage constitutes its structuring principle, enabling the exploration of the theoretical and operative concepts involved in transforming two-dimensional structures into three-dimensional ones. The transition from polygons to polyhedra relates geometry, form, structure and volume. The passage from regular to irregular introduces formal and structural variations, while the relationships between opacity and transparency explore overlapping, depth, visibility and perception. Scale transitions, through regressive and progressive processes associated with fractals, add relationships of repetition, growth, variation and organisation. The Course Unit seeks to understand and master these transitions, recognising how different two-dimensional organisations can be transformed and developed into three-dimensional configurations.

Not applicable

The syllabus explores transitions from two-dimensional to three-dimensional through three complementary areas: Geometric Transitions Two-dimensional to three-dimensional and opaque to transparent transitions; overlapping to construct forms in perspective and establish foreground/background relationships. Transitions in Solids Polygons to polyhedra and regular to irregular transitions; three-dimensionalisation of geometric meshes to understand different processes leading to three-dimensional configurations. Transitions in Scale Regressive to progressive transitions through reduction or enlargement; fractals to explore repetition at different scales, module and modularity, and their relationships. The three areas combine experimentation, understanding and design practice.

The teaching-learning methodologies are based on practical experimentation as a means of understanding processes of transition from two-dimensional to three-dimensional. Exercises begin with previously presented principles and concepts, experimented through the transformation, construction and manipulation of forms and materials. Students learn by doing, observing the changes produced and relating the results to the concepts of each exercise. The passage between different conditions - two-dimensional and three-dimensional, opaque and transparent, regular and irregular, regressive and progressive - enables concepts to be understood through their application. The three-dimensionalisation of meshes, construction of polyhedra, overlapping, changes in scale and exploration of module and modularity constitute operative learning processes. Reflection on the results enables students to understand decisions, correct processes and transfer the principles experimented with to new situations.

Lima, M. (2017). The book of circles: Visualizing spheres of knowledge. Princeton Architectural Press. ISBN 9781616895280. Lima, M. (2014). The book of trees: Visualizing branches of knowledge. Princeton Architectural Press. ISBN 9781616892180. Weyl, H. (2017). Simetria. Ciência Aberta. ISBN 9789896167646. Barbosa, R. M. (2007). Descobrindo a geometria fractal: Para a sala de aula. Autêntica. ISBN 9788575260579.