2024-09-23 17:57:55 : Recent mathematical research has revealed a fascinating new shape called “soft cells.” Characterized by rounded corners and pointed points, these shapes have been thought to be ubiquitous in nature, from the complex chambers of nautilus shells to the way seeds are arranged within plants. This groundbreaking work delves into the principles of tiling, exploring how various shapes can tessellate on a flat surface.
Innovative rounded corner tiles
Mathematicians including Gabor Domokos of the Budapest University of Technology and Economics have investigated how to round the corners of polygonal tiles, resulting in innovative forms that can fill space without gaps. Traditionally, it was believed that only certain polygonal shapes, such as squares and hexagons, would tessellate perfectly. However, a new report in Nature highlights that the introduction of “tip shapes”, with tangential edges that meet at points, opens up new possibilities for creating space-filling tiles.
Transform shape into soft cells
The research team developed an algorithm to convert traditional geometric shapes into soft cells, exploring two- and three-dimensional forms. In 2D, at least two corners must be deformed to form a suitable soft element. In contrast, the three-dimensional shapes were completely devoid of corners and instead had smooth, flowing contours that would surprise researchers.
Soft cells in nature
Domokos and his colleagues noticed that these soft cells are found in a variety of natural forms, including cross-sections of onions and the layered structures found in biological tissues. Their theory is that nature tends to favor these rounded shapes to minimize structural defects that sharp corners can bring.
impact on architecture
The research not only reveals shapes found in nature, but also shows that architects, such as the renowned Zaha Hadid, intuitively incorporate these soft-cell designs into their structures. Discovered mathematical principles can lead to innovative building designs that prioritize aesthetic appeal and structural integrity.
By bridging the gap between mathematics and the natural world, this research opens avenues for further exploration of how these soft cells impact fields ranging from biology to architecture.
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