Abstract
In this paper, the author investigates the role and contribution of pure and applied mathematics to architecture and fine arts in a unified manner. To this end, a thorough and explanatory historical overview of this diachronic and interdisciplinary topic, from the ages of ancient Mediterranean cultures to the so-called western civilization of the late twentieth century is presented. In this framework, the author first examines the fundamental role of traditional mathematics (e.g. Descriptive and Projective Geometry) in architectural design and fine arts, and in the sequel the discussion extends to the outstanding contribution of modern and computational mathematics (NURBS, Fractals, Boolean matrices, Graph Theory, etc.) to these issues. Besides, the important role of computer-aided design (CAD) is mentioned and emphasized. Indeed, CAD is an exceptional scientific and technological achievement, the scientific background of which is essentially a combination of Informatics, Discrete Mathematics and Descriptive Geometry. In addition, various existing problems that sometimes hinder the application of the science of mathematics to architecture and the fine arts are highlighted and demonstrated. Finally, given that the most appropriate mathematical background for the graduate studies in architectural schools along with the schools of fine arts is a very difficult and rather questionable issue, some suggestions are made in order to encourage and strengthen the relationship among applied mathematics, architecture and fine arts.
Highlights
It is well known that the fundamental science of forms and their order geometry contributes to the process of composition and designing in architecture
The idea of fractional dimension had a background that dated back to more than a century before Mandelbrot’s works [Benoit 1975, Brambila-Paz 2017]. As it was already mentioned, fractal geometry is the study of mathematical shapes that display a cascade of never ending, self-similar, meandering details as one observes them more closely
One should elucidate that "Geometric consciousness" is something that is generally approached by all application engineers to a very large extent through intuitive approach, and without the concept of proof with a rigorous mathematical process
Summary
It is well known that the fundamental science of forms and their order geometry contributes to the process of composition and designing in architecture. Leonardo Fibonacci, an Italian born in 1175 AD (2), discovered the unusual properties of the numerical series that bear his name, but it’s not certain that he even realized its connection to phi and the Golden Mean His most notable contribution to mathematics was a work known as Liber Abaci, which became a pivotal influence in adoption by the Europeans of the Arabic decimal system of counting over Roman numerals. It wasn’t until the 1900’s that American mathematician Mark Barr used the Greek letter phi (Φ) to designate this proportion This appeared in the “The Curves of Life” (page 420) in 1914 by Theodore Andrea Cook. Golden triangle is called any isosceles triangle in which the ratio of the long side to the small will be equal to f, whilst the golden rectangle has a ratio of sides equal to Phi
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