post-title How scientists discovered a math equation in rat whiskers

How scientists discovered a math equation in rat whiskers

How scientists discovered a math equation in rat whiskers
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Rats have up to 70 whiskers on their faces, varying hugely in size, and shape. Almost every mammal possesses whiskers, but these rodents are what we call “whisker specialists,” meaning they have super-sensitive, moveable hairs that they use to explore and sense their surroundings.

Rat whiskers can vary hugely. In our recent research, my colleagues and I analyzed 523 whiskers from 15 rats and found that each whisker had a different length and shape. We wanted to investigate more about the shape of these hairs as a first step in understanding what rats feel through their whiskers.

We found that rat whiskers can be accurately described by a simple mathematical equation known as the Euler spiral. It’s an example of how special spiral patterns are found throughout the natural world. And spotting them can help us not only understand nature better, but also improve our own engineering.

The Euler spiral – also called the Cornu spiral, Spiros or Clothoid – is a shape whose curvature changes linearly with its length. It looks quite like an s-shape, where the tips of the “s” carry on curving in to spirals that get rapidly tighter. As a result, aspects of the curve can fit a wide variety of shapes including those that are straight or s-shaped, those that increase in curvature and those that decrease in curvature.

This is why the Euler spiral can be used to describe all types of rat whisker, even though they come in many different shapes. Some are s-shaped, some get more curly towards the tip and some get less curly towards the tip.

Euler spiral of rat whiskers