A group of Hungarian researchers, led by a mathematician, have recently made a groundbreaking discovery that has the potential to revolutionize the fields of geometry, nature, and art. They have identified a new type of geometric shape called “soft cells” that have the ability to completely fill both planes and three-dimensional spaces. What sets these shapes apart is their unique characteristic of being devoid of angles: in two dimensions, the cells have only two corners connected by curves, while in three dimensions, they lack angles entirely.
The research originated from an inquiry into the minimum number of angles required for figures to fill a plane without any gaps. Contrary to previous beliefs that three angles like those found in triangles were necessary, the researchers determined that only two angles were essential. Through further investigation, they developed a mathematical algorithm based on graph theory, particularly Hamiltonian paths, to transform traditional multifaceted shapes into smooth soft cells by eliminating corners.
Not confined to the realm of mathematics, soft cells have been observed in nature, art, and architecture. Researchers have identified similar structures in the shells of nautilus and ammonites, emphasizing their potential for minimal energy consumption due to their lack of sharp corners. In living organisms, soft cells play a crucial role in efficiently filling space, evident in various biological structures such as tissues and blood cells. Architects like Zaha Hadid have incorporated similar forms into their work, showcasing the aesthetic and functional benefits of organic lines.
The interdisciplinary impact of the Hungarian researchers’ work extends to the intersection of nature and man-made objects. Surprisingly, the concept of soft cells has already been intuitively utilized in architectural designs, such as buildings for Cirque du Soleil. These findings highlight the seamless integration of art, science, and design, demonstrating how organic forms can not only be visually appealing but also serve a functional purpose.
Beyond two-dimensional shapes, the researchers, including Domokosh and his colleagues, have also identified the existence of three-dimensional soft cells capable of filling space without any corners. By drawing inspiration from nature and developing algorithms for creating such shapes, they have opened up new possibilities in materials science, architecture, and biology by combining smooth lines with efficient space utilization.