The nautilus shell, with its iconic structure of curved three-dimensional cells, represents a perfect example of how nature often surpasses human ingenuity, even in advanced mathematics.
Despite the capabilities of the human intellect, nature seems to find more efficient solutions, especially in the way it occupies space and solves complex geometric problems. A recent study conducted by researchers at the University of Oxford has brought to light a new class of shapes called soft cells, which offer an innovative solution to the problem of completely filling a space.
Classical human geometry solutions tend to favor shapes with defined angles, such as triangles, squares, hexagons, and polyhedra.
These geometric figures, with sharp angles and flat faces, seem to be the logical choices for filling a space without leaving gaps. However, nature, with its soft and curved shapes, follows different rules. A striking example of this divergence can be observed in the cross-section of a cut onion: instead of right angles or straight lines, there is a set of soft and interconnected shapes that fill the space without leaving gaps.
Similarly, smooth muscle cells are tessellated with elongated and curved shapes, devoid of sharp angles.
These observations demonstrate how nature avoids using sharp angles, preferring more fluid and soft structures. Professor Alain Goriely, an expert in mathematical modeling at the University of Oxford, emphasized how nature not only avoids empty spaces but also sharp angles.
This preference is reflected in natural geometries, which often turn out to be more complex and optimized than those created by humans.
The dilemma faced by mathematicians is: how to fill a space without using sharp angles or flat surfaces? The traditional mathematical problem focuses on how to fill a space with defined figures, such as squares or cubes. However, nature seems to prefer a different solution.
Scholars have discovered that soft cells, with their curved edges and smooth surfaces, minimize sharp angles, allowing space to be filled efficiently.
This principle is present not only in biological structures but also in natural elements such as seashells and red blood cells. The concept of soft cells becomes particularly interesting when moving from two-dimensional to three-dimensional geometry.
For example, in nautiloid chambers, sharp angles are observed in cross-sections, but the internal three-dimensional structure reveals a more fluid geometry without defined edges.
This demonstrates how complex the transition between different spatial dimensions is and how nature has found elegant solutions to these geometric problems. The discovery of soft cells has not only mathematical implications but also practical applications.
These shapes can provide new insights for designing more efficient architectural structures or materials, drawing inspiration from natural solutions to optimize space.
Furthermore, understanding how soft shapes fit so well in nature could open new avenues in the study of biology and natural structures, revealing further secrets about the spatial evolutions of living organisms. Ultimately, nature once again demonstrates its extraordinary ability to solve complex problems with simple and fascinating solutions, often surpassing human mathematical models with structures that combine beauty and efficiency.
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