Thursday, 18 January 2018

Mathemetics of Crocheting

Hi guys!
Have you ever thought that why the heck am I studying Maths during school? Or have you ever thought why and where do I need such complex mathematics?




Well, I have been crocheting since childhood but never thought about it and it only came about much to my surprise that there is a link between crocheting and mathematics!
Yes folks, Its true! In fact all crochet patterns have underlying mathematical structures. The mathematics of crocheting. 


crochet is used to view 3D spaces that are otherwise difficult to understand or view 2 dimentionally. it is used to illustrate hyperbolic and fractal geometry!

In ancient times, making baskets and weaving led to the mathematical discovery in these crafts as the crafts have repetitive patterns.

Some mathematical crochet structures:

 Möbius strips


Mobius stripes in crocheting are nothing than Infinity scarfs! we have made them, used them all along our life but until now, had no idea about their mathematical perspective. In mathematics, a mobius stripe can be defined as a surface with one continuous side formed by twisting the other side at 180 degrees! (Dont get confused, they mean Infinity scarves).

Did you know, Alan Turing, a well known computer scientist, would often knit mobius stripes and other geometric shapes during lunch break!




Mathematics and hyperbolic crochet





Hyperbolic plane is a surface that is always expanding! the space expands and curves away from itself. It is open and infinite and has a very complex geometry. For a crocheter though, creating a hyperbolic pattern is very easy. Just keep on increasing those stitches, like you do in ruffles.




The above piece is just a flat circle that has number of stitches increased in each round so it looks like a giant round ruffle.

As a matter of fact, mathematicians for hundreds of years believed that anything as such was impossible until they accepted that in form of geometry. Because of its complexity, they thought it was not possible to materialize it. However, in 1997 Dr. Daina Taimina, surprised them all with its simplicity through crocheting!




Hyperbolic growth in nature gives rise to the ruffled shapes of coral, kelp, and sea anemone.  The Institute for Figuring created the concept of the Coral Reef with hyperbolic crochet and have been developing this concept since 2005.


Lorenz manifold

Mathematical scientist Edward Lorenz, first studied a system of ordinary differential equations, they are notable for having chaotic solutions for certain parameter values and initial conditions!

Dr. Hinke Osinga(Engineering Mathematics) and professor Bernd Krauskopf have turned the lorenz equation in a real life objects by crocheting computer generated instructions of lorenz manifold!
The overall shape of the surface is created by little local changes: adding or removing points at each step.



Dr Osinga has been able to crochet since she was seven years old , so she noticed that this is exactly the same way that crochet instructions work – by specifying a “surface” (more usually a poncho or baby’s blanket!) in rows, with the number of stitches increasing or decreasing. From there it was a simple step to turn the algorithm into a crochet pattern, and to start to create a real-life Lorenz manifold.

That was clever!

Fractal Crochet





Fractal geometry is a field of maths born in 1970's and is developed by Mathematician Benoit Mandelbrot. Fractal geometry is all about shapes. Fractal is a geometric pattern that is repeated at small or large scale to produce self similar and irreglar shapes and surfaces that are impossible to create in classic geometry. Fractals are irreglar patterns found in nature that are modeled using computers and fractal geometry.





In crochet as you can see, we make certain small unit of a pattern and repeat it over and over again to make the end product that looks like it is made up of smaller sub units. The basic examples are that of doilies, blankets etc.




I hope you found this information as insightful and fascinating as I did. I never knew there is so much to crocheting as this. If you are a crocheter like me, it is a plus point to know more about the science behind the crochet and crochet behind the maths!

Don't keep it to yourself only, Keep pinning, keep sharing!

References:
Happyhart.com
georgemdallas.wordpress.com
www.math.auckland.ac.nz
wikipedia.com

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