# Math in Rats

Christina Sng for Maths@Singapore

Yes, there’s math in rats, specifically their whiskers!

Robyn Grant from the Manchester Metropolitan University discovered that “rat whiskers can be accurately described by a simple mathematical equation known as the Euler spiral…an example of how special spiral patterns are found throughout the natural world.

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.”

Why is this important?

Grant explains, “spotting them can help us not only understand nature better, but also improve our own engineering.”

There are three shapes in a Euler spiral:

1.  Some are s-shaped

2.  Some get more curly towards the tip

3.  Some get less curly towards the tip

Rat whiskers are unique in that they contain all 3 shapes—most natural structures do not display all three shapes.

However, many spirals in nature do get more curved along their length, such as sea shells, sheep and antelope horns, sea horse and lizard tails, and the cochlear in our own ears. They have a  linear radius of curvature along their length, a shape called a logarithmic spiral.

Thanks to DarkCalamari RedRavens @slyfox_2020_photography for making this photo available freely on Unsplash