Patterns in life: rats whiskers (Introduction)

by David Turell @, Sunday, March 15, 2020, 15:39 (196 days ago)

We all know sea shells follow mathematical patterns. Gould's Ph.D. was on certain shells:

https://theconversation.com/how-we-found-a-special-maths-equation-hidden-in-rat-whisker...

"Rat whiskers can vary hugely. In our recent research, my colleagues and I analysed 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.

"Most natural structures don’t display all of these three shapes. But there are many spirals in nature that get more curved along their length. Many sea shells, sheep and antelope horns, sea horse and lizard tails and even the cochlear in our own ears have all been shown to have a linear radius of curvature along their length, making them into a shape called a logarithmic spiral.

***

"Nature is full of mathematical patterns. Given how rat whiskers follow the Euler spiral, and that spirals are so common in nature, we think there’s a good chance the whiskers of other mammals probably follow similar rules and may also be described by Euler spirals. In this way, maths can give us a special insight into how biological structures and systems work."

Comment: It looks as if God is a mathematician, especially as life follows precise patterns which we find when studied..


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