MATHEMATICAL LANDSCAPES: GEOMETRIC PROJECTIONS OF ART

The relationship between visual arts and mathematics has a long historical background. In the 4th century BC, the Greek sculptor Polykleitos mentioned the mathematical proportions of the ideal male body in his notes. Although there is no concrete evidence, the use of the golden ratio can clearly be observed in ancient art and architecture. During the Renaissance period, Luca Pacioli wrote an article titled "The Golden Ratio" (1509), referring to the works of Leonardo Da Vinci. Another Italian painter, Piera della Francesca, incorporated Euclid's ideas on perspective into his works. The famous engraver Albrecht Dürer made numerous references to mathematics in his works. In modern times, with the advancement of technology, computer science has become part of artistic practice. Computers are often used in artistic production involving fractals and in the algorithmic analysis of various artworks through X-ray fluorescence spectroscopy.
M. C. Escher, with significant assistance from Harold Coxeter, extensively used the regular division of the plane and hyperbolic geometry in his works. Additionally, mathematics directly influenced Escher's and many other artists' works through conceptual tools such as perspective types, symmetry analysis, Möbius Strip, recursion, and polyhedra. In Escher's works, besides Coxeter, the influences of certain scientists and artists can be observed periodically. Some of these individuals were personally acquainted with Escher, such as Roger Penrose and Albert Flocon, while others, such as Euclid, Jules Henri Poincare, Frederick Möbius, and Carl Friedrich Gauss, lived before Escher and left lasting impressions on the worlds of mathematics or art.