0, 1, 1, 2, 3, 4, 5, 6, 8, 10, 13, 17, 21, 28, 34, 44, 55, 72, 89, 117, 144, 188, 233, 305, 377, 493, 610, ...............
What does it mean?
We can make a Fibonacci Hyperbolic Fan Shape, using gradual increases, as follows:-
Please click on images to enlarge them.
I've included the higher Fibonacci numbers, just as an academic exercise.
The most exciting aspect of this development is that it is the Algorithm 4 to 5,
ie crochet 3, then crochet 2x in the next stitch.
It is so much easier than the way I've been doing it!
AND it is exactly the Algorithm used by the thousands of ladies who have been crocheting Coral Reef Projects for so many years!
See Facebook......I shall get name asap.....
Thus it may be that someone already knows this Pattern is true for the Fibonacci Series ("egyptian" popped into my mind... silly....)
I have to understand the underlying Principles for myself.
I must say I astonished myself!
Here is more:-
There is more that I can discuss....sometime later.
The Half Fibonacci Series featured in early work of mine when I was trying to elucidate the Bivalves.
Beginning in 23/6/2010 and also in 26/5/2011, 16/6/2011. and 12/12/2012, "responding literally".
Some of my ideas have been mistaken, but it is all part of the Process of discovering stuff for myself.
I shall not repeat all the old stuff; it is there on my blog if anyone wishes to look at it.
Suffice to say, I hope to be using this new easy method in future work; enough suffering with difficult Patterns. I am quite delighted........
And yes, there may be an entirely different Equation which describes the Patterns of these Numbers; only I haven't finished working on it yet.
Here is a bit from this blog 26/5/2010 "hyperbolic crochet on radio"
"Back in August 2009 I managed to catch an interview on ABC Radio National's Artworks program, Amanda Smith chatting with Margaret Wertheim about the Exhibition at Sydney's Powerhouse Museum during Science Week . It was The Sydney Hyperbolic Crochet Reef. Hundreds of people contributed to this colorful show and you can see some of it at http://www.sydneyreef.blogspot.com/
Science meets handicrafts with a view to bring attention to the plight of coral reefs.
When doing craft, time stops.
The algorithm used was " crochet 3 stitches, increase 1 in next stitch. " It's not rigid, you can play with the numbers, to create the shapes of nature."
Then, believe it or not, I caught the moment on radio when Emma Ayres on ABC Classic Breakfast in April gave us the news that Reuters announced the winner of the 2009 Diagram Prize for the Oddest Title for a Book was "Crocheting Adventures with the Hyperbolic Plane" by Dr Daina Taimina. "Splendidly eccentric" said one newspaper, another said "superb juxtaposition...", "the two worlds collide in a captivating and completely breathless way".
You can view this elegant and erudite book on www.amazon.com/Crocheting-Adventures-Hyperbolic-Planes-Taimina/dp/1568814526
and you can see her words on http://www.hyperbolic-crochet.blogspot.com/