Magical Mathematical Sculpture
2008-08-05

Magical Mathematical Sculpture

Consisting of lots of new component elements, sculpture now is more than a form of art. Mathematical Sculpture, as a new branch of sculpture, is studied by many sculptors, or even mathematicians. but till now, there is no work in the scientific literature that provides a systematic analysis of the possible relationships between Mathematics and Sculpture. That's OK. Our job is just to observe and enjoy them. But first, let's have a general understanding of Mathematical Sculpture.

Mathematical sculpture, also called Geometric Sculpture, is a term of all the sculptures for which the application of Mathematics becomes essential in their conception, design, development or execution. In order to include a given work in this typology, some mathematical concept or property must be significantly essential.

Works by Sculptors of constructive geometric forms often deal with patterns and relationships derived from classical ideals of balance and symmetry. Mathematical yet organic, these abstract forms invite the viewer to partake of the geometric aesthetic. They usually use a variety of media, including paper, wood, plastic, metal, and assemblages of common household objects to express the idea in their process of design.

As an example, here are two sculptures based on the same concept, that of ruled surfaces, that is, the surfaces formed by joining the positions obtained by moving a straight line in space However, the complexity of both sculptures is clearly different. The work shown in figure 1 is very simple whereas the sculpture shown in figure 2 is very complex. The latter sculpture is an extension of the concept of ruled surface, to the use of the movement of any curve for the formation of the surface. 

Figure 1: Javier Carvajal, series: Parallel Slices. Case of 75ş of section and 180ş of total turn. Front view.
Figure 2: Javier Carvajal, Side view of the same sculpture.

If we pay attention to the types of sculpture included in the pictures below, the design of mathematical sculptures makes use of concepts relative to many mathematical fields: Geometry, Differential Calculus or Vector Calculus, Algebra, Topology, Logic, etc. And this is often considered as a simple classification of mathematical sculpture. 

From Left to Right
Figure 3: Figure 22: Eduardo Chillida, Elogio del horizonte, Gijón, Spain
Figure 4: "Cohesion" (Fall 2002) - bronze, 12" tall
Figure 5: Ferguson et al. 1999, Wagon 1999
Figure 6: Bathysphere, George W. Hart


Note that some sculptures explicitly show this mathematical nature; an example of this could be the figure of a polyhedron; however, in other works these concepts are only present in an implicit or hidden way, such as the composition shown in figure 7, in which the mathematical conception is implicit in the sculpture's design. So it is difficult to delimit the concept of mathematical sculpture and whether a particular work may be considered as a mathematical sculpture. 

Figure 7: Javier Carvajal, Two columns of inverse rotation. Series of sculptures: Solominic Columns. 1991-1994. 

Classical forms are pushed in new directions, so viewers now can take pleasure in their Platonic beauty yet recognize how they are updated for our complex high-tech times. The use of the computer by many sculptors has allowed the development and evolution of mathematical sculpture. In addition, the computer has allowed the correct execution of very complex sculptures. An illustration of this can be seen in Figure 8, which shows a work by Bathsheba Grossman with a very complex geometry. 

Figure 8: Bathsheba Grossman. Seven spheres.

Great works invite contemplation, slowly revealing their content; some viewers see them as meditation objects. When we're standing in front of the sculptures, if a lively dancing energy moves within each piece and flows out to us, then we get it. All the basic things about mathematical sculpture above will help you appreciate them better. Then you'll see the crystalline purity, conundrum of complexity and stark simplicity that the sculptures present.