Buzz
Scientists have found that epithelial cells, which form the outer layers of many human organs, adopt a unique geometric structure called the scutoid to enable tissue curvature. This breakthrough was made by researchers at the University of Seville.Unless you've been completely out of the loop, you’ve likely come across the buzz about the latest geometric revelation: the scutoid. A group of biologists from the University of Seville developed a model of the scutoid to understand how epithelial cells organize themselves to create protective layers in skin, organs, and blood vessels.
Using mathematical principles, the team proposed the existence of a natural shape essential for building complex multicellular structures. Upon realizing this shape was previously unknown in geometry, they named it the scutoid, inspired by the scutellum, a beetle’s thorax segment that bears a slight resemblance to the newly identified form.
The scutoid serves as a fascinating example of how new shapes are discovered, offering insights into their origins and the reasons behind our pursuit of them.
The simplest way to uncover shapes is by observing them in nature. Take the hexagon, a six-sided figure found in soap bubbles, honeycombs, and even the clouds of Saturn. In his Nautilus article, "Why Nature Prefers Hexagons," Phillip Ball delves into why this shape is geometrically optimal for various functions. The hexagon evolved through natural processes, and humans later gave it a name.
While some shapes are rare in nature, they arise easily from geometry or even imagination. Right angles, for example, are uncommon in the wild. A walk through nature won’t reveal squares or rectangles. Studies suggest humans may be naturally inclined to favor curves over straight lines. Despite this, we still design cubes and use them to reshape our environment.
There’s a gap between shapes that can be imagined and those that exist or can be replicated in nature. Perfect circles, for instance, don’t exist in the physical world. Mathematically, we can define a circle as a set of points equidistant from a center, but in reality, even the most precise circles and spheres fall short of perfection. For example, the quartz gyroscopic rotors in NASA's Gravity Probe B are less than three ten-millionths of an inch from perfect.
The scutoid, on the other hand, appears to be a real geometric entity. While we can’t see it directly, scientists have used mathematical models to describe it as a solution to a biological challenge. Even if future discoveries replace the scutoid, its geometric existence remains undeniable.
To recap, shapes can be discovered by observing them in nature, deducing their presence through natural phenomena, or exploring pure mathematical concepts. While rare, shape enthusiasts sometimes uncover a new type of pentagon or even an entirely new category of solid shapes.
Feel free to explore and see what you can uncover — but keep in mind that many mathematical shapes are already documented. The trapezo-rhombic dodecahedron has been claimed, and Clickhole has already reserved the Triquandle.
Optical illusions like the Penrose triangle play on the same visual cues that make reversing letters a common error for young students. While a p and a q are clearly different on paper, they can appear as two perspectives of the same 3D object. The Penrose triangle, though impossible to construct in real 3D space, is perceived as a three-dimensional figure and retains the shape of a triangle. As Lionel and Roger Penrose demonstrated, such objects can be discovered and named — even if Oscar Reutersvärd conceived it decades earlier.
