Abstract at English
The main objective of this doctoral thesis is to study the kind of Art that we have called "Mathematical Sculpture" and classify it as exhaustive and complete as possible. There is no study in the scientific literature that offers a systematic classification of Mathematical Sculpture. That led us to choose the developed of this taxonomy as the basic objective of this research. Moreover, this give characteristic of innovation that must be present in all doctoral thesis.
We have started researching in general the relationship between Mathematics and Art and in a special manner the relationship between Sculpture and Mathematics. To achieve it we have done a systematic historical analysis.
Then in order to develop the taxonomy of a set of elements, the first step consists in identifying its component elements. For that end, first we have to define the term Mathematical Sculpture. All the sculptures for which the application of Mathematics becomes essential in their conception, design, development or execution belong to this typology. This characteristics could ranged from the simplest geometry to the most complex non-Euclidean geometry or topology.
On the other hand, we think that the best way for classifying Mathematical Sculpture consists in establishing as principal groups, different areas of Mathematics and then subdividing these groups according to the more important Mathematical concepts used in the different types of sculpture's design. We have proposed the next as main groups: Geometrical Sculpture, Sculpture with Concepts of Calculus, Sculpture with Algebraic Concepts, Topological Sculpture and Sculpture with different Mathematical Concepts.
The main interest of this research is to contribute to settle down the study of Mathematical Sculpture, so as to allow for its incorporation in higher education syllabi, either as a separate course or as a part of the course contents of other courses dealing with the relationship between Mathematics and Art.