Who Was Fibonacci?

The Fibonacci Series was named after Leonardo of Pisa, a member of the Bonacci family.
Born in 1170 and died 1250.
He was educated in North Africa and studied mathematics with foremost scholars. His father, Guilielmo, held a diplomatic post. In 1200 the son ended his travels and returned to Pisa.

Leonardo introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. He also introduced the Fibonacci Series to western European Mathematics.
All this info I gleaned from Dr Ron Knott's website hosted by the Mathematics department of the University of Surrey, UK.
www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

Thus the Fibonacci Series was not invented by Mr Bonacci.
I believe that in those days The Middle East, including Baghdad, was the pinnacle of Art and Science. My guess is that the Fibonacci series goes back even further, to ancient Vedic times, when there were wise humans who understood the secrets of nature.

The best evocation of Vedic times that I have encountered is given by the Siberian Wisewoman, Anastasia, in the Ringing Cedars of Russia series, 9 books, by Vladimir Megre.
http://www.ringingcedars.com/ (also .au or .ru)
Especially see Book 6, "The Book of Kin", from page 94 for several chapters.

I would like to think that enough people care about Mother Earth, to help to save her and her beauty and magnificence. May it be so.

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/

In fact, Dr Taimina has gracefully corresponded with me by email and she gave me a lovely site to follow http://www.hellejorgensen.typepad.com/

Hello Emma! I believe our ABC Radio has the most wonderful music and radio journalism - I listen whenever I can -- and people all over the world listen online www.abc.net.au/rn or www.abc.net.au/classic

I describe my own work as "simple and curious".
Cheers to youse all!

How did I begin this adventure? **

In the 1970s and 1980s I read "The Secret Life of Plants" and :Secrets of the Soil" by Peter Tomkins and Christopher Bird. In Chapter 9 of the latter, The Vortex of Life, the Fibonacci series of numbers, 1, 2, 3, 5, 8, was mentioned. ....internal corkscrew patterns... similar to seashells and animal horns....The Vedas describe the Universe as ellipsoidal. In the 1930s a professor of Mathematics said the entire universe revolves around a geometrical form which is a rectangular hyperbola. Schwenk wrote -vortexial formative processes in nature .......
Reich wrote of the creation of matter from the throat of cosmic vortices such as nebulae.....

Back then, I thought how good it would be to make a Nautilus shell form in accordance with the Fibonacci series. Curiosity compels one to follow certain directions.

The big clue was an article in my favourite UK magazine, Resurgence. http://www.resurgence.org/ in the July/August 2007 issue, on page 43. I quote verbatim:-
"Ïn 1997 Dr Daina Taimina discovered how to make models of the geometry known as hyperbolic space using the art of crochet. Until that time most mathematicians believed it impossible to construct physical models of hyperbolic forms, yet nature has been doing just that for hundreds of millions of years. It turns out that many marine organisms embody hyperbolic geometry, among them kelps, corals, sponges and nudibranches."
The website was given of The Institute for Figuring http://www.theiff.org/
Co-directors Margaret and Christine Wertheim are curators of a splendid exhibition of Crocheted Hyperbolic Coral Reefs. (Also check out the computational origami of Robert Lang, laser physicist!). There I found more from Dr Taimina - "as you move away from a point, the space around it increases exponentially....knit or crochet...ruffle and crenellate. Íncrease 1 stitch in every 3, you get a pseudosphere- the hyperbolic equivalent of a cone.....if you increase once in every stitch it becomes increasingly crenellated....you can increase 2 or 3 times in every stitch...."

Thus I also began the adventure, trying to figure out how to crochet the Fibonacci Series.

More in the next episode of blogspot, from Tiiu V.

Variations on a Hyperbolic Theme **

Following on from the previous posting:-

To make a larger and softer model of a snailshell one can crochet or knit one or more plain rows between each Pattern row.

If an even number of plain rows are made, then here is the simple pattern:-

1
(1 x 2) + 0
(1 x 2) + 1
(2 x 2) + 1 ...............................makes 5
(5 x 2)+ 3 ...........................................13
(8 x 2) + 5 ...........................................21
(13 x 2) + 8 .........................................34
(21 x 2) + 13 .......................................55
(34 x 2) + 21 .......................................89
(55 x 2) + 34 ......................................144
(89 x 2) + 55 ......................................233
(144 x 2) + 89 ....................................377
(233 x 2) + 144 ..................................610
(377 x 2) + 233 ..................................987
(610 x 2) + 377 ..................................1597
(987 x 2) + 610 ..................................2584 etc




If 1 or an odd number of plain rows are inserted then the pattern needs to alternate:-
1
(1 x 2) + 0
1 + (1 x 2) ............................Makes 3
(2 x 2) + 1 ....................................." 5
2 + (3 x 2) .......................................8
(5 x 2) + 3 .......................................13
5 + (8 x 2) .......................................21
(13 x 2) + 8 .....................................34
13 + (21 x 2) ...................................55
(34 x 2) + 21 ..................................89
34 + (55 x 2 ).................................144
(89 x 2) + 55 .................................233
89 + (144 x 2) ...............................377
(233 x 2) + 144 .............................610
233 + (377 x 2) ..............................987
(610 x 2) + 377 .............................1597
610 + (987 x 2) ............................2584 etc.

Half treble crochet stitch
wool round hook, hook into loop, wool round hook, pull through all 3 loops.

To knit, use the same patterns but work backwards and decrease in accordance with the Fibonacci series by knitting 2 together.

With variations, the sky is the limit.
Someone could even make a huge model stuffed with pillows.
I live in a caravan on 2 acres, without electricity or a car, so I prefer small models.

One can embroider stripes up the shape.
There is a species, Nodilittorina tuberculata, which has a pattern of knobs along the spiral. I tried to copy this by regularly bunching up the edge as I sewed up.
Janthina is pale violet on top and dark violet underneath.

On Feb 14 this year, Valentine's Day, I noticed that this very same hyperbolic shape for snail shells can also configure into a bivalve! One coils the shape from the 2 pointy edges. When I have photos of complete models I will post them.

I am told that thousands of people are making crocheted hyperbolic shapes all over the world and I am glad to discover more ideas.

Enough for now from Tiiu V.

PHOTO GALLERY OF ALL MY SHELL MODELS, so far **.

The shapes in the top photo were knitted and the other photo shows all crocheted shell shapes, all iaw the Fibonacci Series of numbers.

I wanted the purple ones to look like Janthina janthina.

I'll post a larger Pattern for the numbers, just for good measure. .......

Funny! It ended up at the top of the page. I can't quite figure it out how to manage this blog, but it is OK anyways. Cheers from Tiiu V.

More Seashell Photo Gallery **

It took quite a bit of perseverance to sew up and pad the more complicated models, but it is not impossible!
The yellow is 4 ply equivalent cotton and the edge was made in blue sewing machine cotton.

Very fine tapestry wool, 2 ply, was used for most of the models. Half treble crochet was my preferred way. Next post will be photos of all the shapes of shells that I have made up to date, including the knitted ones.

Photo Gallery of Models of Seashells, crocheted and knitted. **

Hello

Here goes and I hope the images come up OK.

Instructions were given in the previous posting of how to make them.

......................................................................................................................

I see the photos have arranged differently from what I expected!

Anyway it is possible to see what the crocheted form looks like before and after being sewn up and padded.

Instructions for Making a Model of a Mollusc **

1. CROCHET

You can use any kind of yarn - eg No 8 crochet cotton, any ply wool

Use crochet hook of desired size - eg No 2

You can do any kind of crochet stitch - single, double, half treble, treble, double treble, etc.

To begin, crochet 5 chains

crochet into 3rd loop twice -makes 2 stitches

****Begin every row with 2 chains.

row 1........ crochet in 1st loop x2, crochet 1x in next loop -makes 3 stitches

row 2........ crochet x2 into next 2 loops, crochet 1x into next loop ---makes 5 stitches

row 3........ crochet x2 into next 3 loops, crochet 1x into next 2 loops ---makes 8 stitches

row 4........ crochet x2 into next 5 loops, crochet 1x into next 3 loops ---makes 13 stitches

row 5........ crochet x2 into next 8 loops, crochet 1x into next 5 loops ---makes 21 stitches

row 6........ crochet x2 into next 13 loops, crochet 1x into next 8 loops ---makes 34 stitches

row 7 ........crochet x2 into next 21 loops, crochet 1x into next 13 loops ---makes 55 stitches

row 8........ crochet x2 into next 34 loops, crochet 1x into next 21 loops ---makes 89 stitches

row 9........ crochet x2 into next 55 loops, crochet 1x into next 34 loops ---makes `144 stitches

row 10........ crochet x2 into next 89 loops, crochet 1x into next 55 loops ---makes 233 stitches

This is enough to make the blue green model of snail in photo this post.

Fold crochet work in half and sew it up, leaving opening such as a snail has. The work configures into a spiral which needs to be gently padded as you go.

You can use any kind of padding such as wool fleece or cotton wool, etc.

2. KNIT

You can use any kind of yarn eg crochet cotton or wool and any suitable size knitting needles. The brown snail in photo was made in 8 ply wool; use No 8 or 11 or so size needles.

row 1........ cast on 233 stitches

row 2........ knit 2 tog x89, knit 55

row 3........ purl 2 tog x55, purl 34

row 4........ knit 2 tog x34, knit 21

row 5........ purl 2 tog x21, purl 13

row 6........ knit 2 tog x13, knit 8

row 7 ........purl 2 tog x8, purl 5

row 8........ knit 2 tog x5, knit 3

row 9........ purl 2 tog x3, purl 2

row 10...... knit 2 tog x2, knit 1

row 11....... purl 2 tog x1, purl 1

row 12....... knit 2 tog

row 13....... finish off.

Fold in half and sew together, gently padding as you go

and you have a nice simple snail model just like the brown model in the photo image here,

in accordance with the Fibonacci series of numbers.

If you are more adventurous, you can make models with 377, up to 1597 stitches, so long as the Pattern in blogs 2 and 3 is followed. There will be more photos in the next blog.

Good luck and happy crafting. from Tiiu V

Fibonacci Series Pattern ** **

Hello again,

The last post should have included a photo image.

Here it is. The Fibonacci series Original Pattern for crocheting or knitting a snail shape.
There is an entirely different Pattern for making a model of a vortex or series of ripples.

They say an image is worth a thousand words.

Click on photo to print it out.

More next time

from Tiiu V.