Mathematicians have discovered a simple principle that allows spiders to find out which part of their trapping net the next victim has fallen into, and also use the web to constantly collect information about the environment. Their findings were published in the SIAM Journal on Applied Mathematics.

"The spider web is a natural, very lightweight and elegant structure that has tremendous strength in relation to its mass. Until now, we did not even have a simplified mechanical model that would describe the operation and nature of this two-dimensional vibrating system," one of the its authors, professor of mathematics from the University of Udine (Italy) Antonio Morassi.

The cobweb has attracted the attention of a wide variety of scientists for many decades. For example, engineers and mathematicians are interested in the principles of the structure of the web, biochemists and chemists - its composition and the possibilities for using its components in practice, and evolutionists - in how spiders learned to weave such trapping webs.

Scientists hope that these experiments will help humanity "copy" some of the inventions of nature and teach us to use them for our own purposes. For example, in July of this year, geneticists decoded the genome of Madagascar spiders, weaving the most durable trapping webs on Earth, and discovered a unique protein that makes their trapping nets ten times stronger than Kevlar.

Morassi and his colleague Alexandre Cavano from the University of São Paulo (Brazil) have found a mathematical answer to one of the main biological mysteries - how spiders almost instantly determine which part of their web the next victim has fallen into, and also distinguish it from random blows of wind or blows of branches …

## Hunting mathematics

The web is woven from radial and spiral fibers, whose composition and function differ. The latter consist of a "soft" variety of silk, which sticks to the victim and prevents it from leaving the hunter's net. Radial filaments are made up of an extra strong variation of these protein fibers that hold the web in place and prevent it from warping.

In the past, mathematicians have tried to represent them as one-dimensional structures along which vibrations generated by a spider's lunch or random processes propagate. These models did a good job of describing how different types of oscillations arise, but they were not able to explain how exactly the eight-legged predator determines their type and localizes their sources.

Cavanaugh and Morassi solved this problem by imagining the spider web as a kind of two-dimensional membrane, which consists of many intertwined fibers of two types. Different types of vibrations propagate along the surface of this membrane. This approach allowed them to put themselves in the shoes of a spider lurking in the center of the web, and to understand how it "hears" its victims, wind and other sources of noise.

Calculations have shown that the predator determines the position of the prey by comparing how much the tension force of different radial fibers touching its legs changes. The eight legs of the spider, according to the researchers, are quite enough to unambiguously determine the source of the vibrations and understand what causes them.

Similar mathematical principles, according to Morassi, can be applied to create supersensitive pressure sensors and other sensors, similar to the principles of the device on the web, as well as in order to solve other practical problems.