Unpacking the Fibonacci Series and the First Model **

Back in July 2007 I needed to find a sequence within the series which was amenable to crochet or knitting patterns. Above is a photo of a page from my Journal to illustrate. Another page from my Journal is above it. Click to enlarge to full size. Then go back to main text.

It was evident that 2 times F(n-2) plus F(n-3) was the Pattern.

eg 610=2x233+144

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The yellow and beige model was the very first one I made-

in the photo it is 377 stitches crocheted on the outer edge.

The model below is 144 stitches on the outer edge.

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The second photo is of the models folded in half.

The 144 model looks like a bracket fungus, or like a pouch!

One thinks of endoderm, ectoderm etc and invagination--

the beginnings of cell division, maybe!

At the time I only knew to crochet in a circle was not the way to crochet a seashell,

so I had to make another Pattern and this is the one which works:-

It forms a hyperbolic geometric shape which folds in half to configure neatly into a shell spiral, as simple or a complex as one wishes to make.

The very first model of a seashell I made was a left hand spiral. I was disappointed, as the real thing was right hand spiral, so I taught myself to crochet left handed. It was a good exercise. I notice that many of the young girls on the school bus are left handed and one needs to know how to do it their way if I were to teach them

Then I realised-- all one needed to do was fold it back the other way to get the right hand spiral.

There was a moment when I was gazing at the folded up model and I realised that the opening was just where a snail has its opening. It was OK

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***Next post is of Bivalves. They are made iaw a Pattern exactly half of the above design.

Fun and a bit tricky to make.