Mathematics for Design
The explicit use of mathematics in design is not an innovative concept by itself. Already during the Renaissance period, Leonardo da Vinci, who was both artist and scientist, introduced the Golden Number and the perspective effect in many of these works, such as The Man of Vitruvius, around 1490. Throughout history, there are many examples where mathematics has revolutionized art and design. More recently, the Japanese Azuma Hideaki became interested in origami, creating a connection between his mathematical studies on the theory of varieties and this ancient art, in order to reveal a new beauty on it. From that, its origami are not necessarily built from a paper square, folds along several symmetrical lines and right triangles, as the “tradition” wants. His work Convolution was Azuma’s starting point in his personal world of folding.
Mathematics covers several topics such as geometry, algebra or analysis. Studying them often allow the mathematician to visualize the results of his work. Then, it is very common that the aesthetic aspect of these discoveries turns out to be strikingly beautiful. Geometric shapes obviously translate in a visual way this aesthetic appeal explicitly. From the “simple” regular polygons of Plato to the “complex” fractals of Mandelbrot, the mathematical objects covered by geometry may catch the attention because of the variety and beauty of their structures, as well as the depth of their details. Another geometrical important point to emphasize in design theory is the concept of dimension, in the vector sense of the term. Mastering dimension 2 for flat exercise, dimension 3 for volume work, and the perspective effect to give a 3D illusion on a flat structure is necessary. The knowledge of higher dimensions, more abstract by their definition, also allows to elevate the design to a very surprising degree of aesthetics. On a different level, some functions or number theories graphs, like the prime numbers distribution graph, can also reveal interesting features to explore. Finally, besides the direct visual aspect of mathematics, we will not forget to note their obvious importance in the establishment of methods and construction rules necessary to design, as well as the possibility of putting them at the service of the customization request - major challenge of our time - with, for example, models with variable parameters.
The first mathematical theory explored for the 5922 project is the famous Pascal’s Triangle. Named this way in honour of the French mathematician Blaise Pascal, who dedicated it the Treaty of the Arithmetical Triangle in 1964, this triangle was studied several centuries before him in India, Persia, China, the Maghreb, Germany or Italy. It was also found in the Jade Mirror of the Four Unknowns from the Chinese mathematician Zhu Shijie in 1303, which revolutionized Chinese algebra. This triangle, which is built from Pascal’s formula, presents the binomial coefficients and hides many properties. We find, for example, the Fibonacci sequence, the triangular numbers, or even the Fermat’s theorem. Thus, by approaching this omnipresent mathematical object from different angles - in the spirit of the 5922 project - and by working with different supports, it is possible to come up with designs that reveal very astonishing aesthetic and even functional qualities.
The 5922 project might be able to demonstrate the added value that mathematics can bring to design.