Most of us have been stung by a bee, bitten by an animal, or scratched by a thorny bush. But very few of us have probably taken a close look at nature’s painful pointed tips. At first glance, they both look and feel like the cone-shaped needles we know from the doctor’s instrument tray. In reality, many natural tips are rounded and curve gently rather than ending in a sharp tip. Mathematically, the shape can be described as the height being proportional to the square of the radius (height ~ radius²). This results in a rounded shape—called a parabola—where the tip is not sharp but gradually becomes steeper away from the center.

Scientists have long assumed that the rounded shape is the result of evolutionary optimization, because it penetrates the skin more easily than a perfect cone, and that organisms have thus evolved their defenses toward the most effective form.

The rounded shape is also more robust, less prone to breaking, and distributes forces more evenly throughout the tissue. But according to Kaare Hartvig Jensen, associate professor at DTU Physics, evolution is likely not the sole explanation for the shape:

“There is a general notion that almost everything in nature exists for a reason. A previous study from 2024 argues that the rounded tips of teeth are due to evolution. But if you look at an unused tooth, it does not necessarily have that shape, and if you observe the shape later in the organism’s life, the parabola will emerge. This suggests random mechanical wear. We cannot rule out the role of evolution, but random processes are an equally good explanation.”

The researchers’ findings were recently published in the renowned scientific journal PNAS in the article ’The geometry of Nature’s stingers is universal due to stochastic mechanical wear’.

When Wear Shapes Pointed Tips

To test the hypothesis regarding mechanical wear, Kaare Hartvig Jensen and his research colleagues conducted a simple yet effective experiment. A handful of sharpened pencils were placed on a plate atop a shaking machine, where they were shaken around for 4.5 hours and constantly collided with one another—as if they were little gladiators in an arena.

In addition, the researchers also carried the pencils around in a small box in their pockets, again to expose them to random collisions and movements. This was not only practical but also a deliberate choice. The experiment was meant to be easy to relate to—and, in principle, something one could carry around in one’s own pocket and observe.

The pencils function as a so-called biomimetic model—that is, their tips mimic natural structures such as teeth, thorns, and stingers. Specifically, they represent an “unused” tip, as seen, for example, in the teeth of young animals. And the result is remarkable. For no matter how sharp the pencils were to begin with, their tips, as a result of the collisions, developed the same rounded parabolic shape. A shape that has otherwise often been explained as a result of evolution.

“This points to something more fundamental: that random processes in and of themselves can lead to a universal form. The parabola is a stable shape across scales, from a thorn to an elephant’s tusk. It appears to be a coincidence that this shape is also the most effective for biting, stabbing, or tearing. The tips are thus not necessarily designed perfectly from the start—they become so through random wear,” says Kaare Hartvig Jensen.

Stone Age Tools and Pine Cones

The project is part of a larger research initiative supported by the Villum Foundation, which investigates so-called biological morphogenesis—that is, how organisms develop their forms.

The idea for the project arose as an extension of this work. The researchers’ ultimate goal is to understand which microscopic mechanisms—all the way down to the atomic level—can give rise to the patterns observed in nature.

In the future, the researchers hope to be able to study biological tips more directly in the laboratory. Unlike pencils, natural structures are rarely homogeneous or isotropic—that is, they are not the same in all directions. An elephant’s tusk, for example, has a hard, compact outer surface, while the structure inside is softer and more complex, with microscopic channels.

The pencil experiment shows, however, that wear leaves measurable traces in the shape, making it possible to deduce information about how an object has been used. In archaeological contexts, where it can be difficult to reconstruct how stone tools were used, such traces can be crucial.

“By analyzing wear patterns and the degree of rounding, we can begin to quantify the use—not just observe it. We can say something about how much a tool has been used and what it has been used for. In this way, even small changes in a pointed shape can provide insight into the life of an object or organism,” says Kaare Hartvig Jensen.

In addition, the experiment prompts reflection on the significant role physical and random processes play in nature.

“Nature can utilize physical processes. A good example is the pine cone: When it is wet, it is closed, but when it dries, it opens automatically and disperses its seeds. This is not an active biological process, but a physical effect driven by moisture and drying. It shows that not everything in nature is controlled by genes and proteins. Sometimes random and physical processes are both crucial and functional—and it’s wonderful to see how even random processes can be an advantage,” says Kaare Hartvig Jensen.

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About the research

Read more about the experiments and results in the researchers’ own blog post: Universal Shape of Pointed_Tips

Or in the scientific article published in the journal *Proceedings of the National Academy of Sciences* (PNAS): The geometry of Nature’s stingers is universal due to stochastic mechanical wear

The research is supported by the Villum Foundation.