Recent mathematical research has revealed a fascinating new class of shapes known as “soft cells”. These shapes, characterized by rounded corners and pointed tops, are recognized as prevalent throughout nature, from the intricate chambers of nautilus shells to the way seeds are arranged within plants. This groundbreaking work deals with the principles of tiling, which explores how different shapes can be formed into a tessellation on a flat surface.
Innovative laying of tiles with rounded corners
Mathematicians, including Gábor Domokos from the Budapest University of Technology and Economics, examined how rounding the corners of polygonal tiles can lead to innovative shapes that can fill space without gaps. Traditionally, it was thought that only certain polygonal shapes, such as squares and hexagons, could tessellate perfectly. However, the introduction of “bump shapes,” which have tangential edges that meet at points, opens up new possibilities for creating space-filling tiles, a new Nature report points out.
Converting shapes into soft cells
The research team developed an algorithm that transforms conventional geometric shapes into soft cells, exploring both two-dimensional and three-dimensional shapes. In two dimensions, at least two corners must be deformed to create a correct soft cell. In contrast, three-dimensional shapes can surprise researchers with a complete lack of angles, instead taking on smooth, flowing contours.
Soft cells in nature
Domokos and his colleagues observed these soft cells in a variety of natural formations, including cross-sections of arches and layered structures found in biological tissues. They theorize that nature favors these rounded shapes to minimize the structural weaknesses that sharp corners can introduce.
Implications for architecture
This study not only sheds light on the forms found in nature, but also suggests that architects, such as the famous Zaha Hadid, have intuitively used these soft cell designs in their structures. The mathematical principles discovered could lead to innovative architectural designs that prioritize aesthetic appeal and structural integrity.
Conclusion
By bridging the gap between mathematics and the natural world, this research paves the way for further research into how these soft cells can influence fields ranging from biology to architecture.
