A Comparison Between Fourth Dimensional Geometry and Cubist Art Forms
The world around us exists with three different spatial dimensions. However, from as early as the 1880’s, mathematicians have pondered the existence of a fourth spatial dimension, and even higher dimensions beyond that [1]. Yet, living in the third dimension, we are not able to perceive object in hyperspace. In order to view such an […]
Quasicrystals: Symmetry and Characteristics and Their Application as an Art Form
Part of artist M.C. Escher’s work focused on tessellations in the second dimension, many of which would periodically tile the plane. However, tilings can also be aperiodic, not having a set repeating pattern. Roger Penrose and his Penrose tilings are examples of these types of tiles. Penrose tilings have another characteristic about them as well: […]
Fractal Artwork: Dimension and Complexity as a Guide for Aesthetics
Jackson Pollock is an artist famously known for his technique of paint dripping to create various works of art, using a pouring technique to create designs as opposed to more Euclidean shapes produced by brush strokes. Due to this method of painting and the results it produces, Pollock’s works can be described to be fractal […]
Repetition and Order: How Space Filling Fractal Curves Exhibit Aesthetics
A space filling curve is a line that can be drawn continuously, without lifting a pen if done on paper. However, when this curve is drawn infinitely, it completely fills a square without any holes [1]. One example of a curve like this is the Hilbert curve. To produce the Hilbert curve, take the n […]
Escher’s Tessellations: Symmetry and Groups Expressed as Art
Artist M. C. Escher’s work, “Regular Division of the Plane,” extensively uses different tessellations that are altered into various drawings. These tessellations, or shapes that tile a plane, tended to be constructed out of altering various polygons, such as triangles and squares. In one technique, Escher would find polygons that tile a plane, and then […]
Connections Between Art and Mathematics Through Education and Aesthetics
On the surface, the fields of mathematics and the arts do not seem likely to fit well together. The former is known more for its logical composition, and the latter for aesthetics and design. However, this is not always the case. More and more, many people are coming to realize the connections that can be […]
