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Nudibranch 04-19-2012 03:00 PM

Lobachevsky redux
 
FrankLee asked for another layer of the onion when I introduced myself (intro thread) and headered it "Lobachevsky love."

Lobachevsky was a 19th century mathematician who created and published a geometry in which Euclid's Fifth Postulate did not hold. In doing so he laid out the basis of hyperbolic geometry.

Hyperbolic geometry is what accounts for things such as the form and branching of sea corals, the sprawling of the internet, and many other geometric forms based on exponential patterns of increase.

Here is a nice illustration:
http://www.nature.com/ncomms/journal...ms1063_F1.html

And an outstanding introduction using hyperbolic geometry and crochet:
http://www.mnh.si.edu/exhibits/hreef/

http://www.theiff.org/

The interesting thing is that very simple increases, systematically and carefully managed, can explode into whole new, vast, and stunning forms. That's where I see it overlapping with love. Frank observed what he called something like a "poly obsession with geometry," and I'm paraphrasing there. Yes, I think many of us intuit that there are many other patterns of increase possible than just two people getting together and making babies and watching human numbers double more rapidly every century.

http://www.albartlett.org/presentati...on_energy.html

Frank, thanks for asking.

NovemberRain 04-20-2012 05:34 AM

hurray FrankLee :D

Thanks for all those links, Nudibranch. I have an appreciation for math, having been surrounded by mathematicians for much of my time on the planet. If I work very hard, I can wrap my mind around some of it, but it is so not my forte.

Nudibranch 05-01-2012 06:36 PM

November, in my view the trick is to get the shape and form of the math, the way it plays out in successive iterations (in the case of hyperbolic math).

What is often called math that puts people off is the symbolic representations of those shapes and forms.

This is why I often point people to hyperbolic crochet, particularly the crocheted coral reefs. How patterns of increase can yield magnificent new forms in nature is a beautiful example of how math plays out in reality...without dragging folks into a bunch of symbols they may not be wired to understand.

To put it another way, you don't have to understand the formulas to appreciate the exquisite beauty of a Mandelbrot set...or a nudibranch's petals!

http://animalworld.tumblr.com/post/2...olus-cristus-c

Thanks, Nov.


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