Mathematicians have identified a new class of shapes that "tile space without using sharp corners."
From bathroom floors to siding on buildings, it's common to cover areas without gaps by arranging shapes with straight edges and flat surfaces. In the natural world though, those kinds of shapes are rare. Patterns like those in muscle tissue are created with flowing curves, rounded surfaces, and almost no sharp angles. But the mathematics of these "soft shapes" have been a mystery until now.
"Nature not only abhors a vacuum, she also seems to abhor sharp corners," says University of Oxford mathematician Alain Goriely who, with colleagues from the Budapest University of Technology and Economics, discovered the new shape class called "soft cells."
From Oxford University:
In 2D, these soft cells have curved boundaries with only two corners. Such tiling patterns are found, among others, in muscle cells, zebra stripes, the shapes of river islands, in the layers of onion bulbs, and even in architectural design.
In 3D, these soft cells become more complex and interesting. The team first established that, in 3D, soft cells have no corners at all. Then, starting with conventional 3D tiling systems such as the cubic grid, the team showed that they can be softened by allowing the edges to bend whilst minimising the number of sharp corners in this process. Through doing this, they found entire new classes of soft cells with different tiling properties.
Professor Gábor Domokos said: 'We found that architects – including Zaha Hadid – have constructed these kinds of shapes intuitively whenever they wanted to avoid corners.
Previously:
• How math people look at math, and why it works
• Revisiting Make:'s weekly Math Monday column
