Tuesday, May 25, 2010

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

Wednesday, May 19, 2010

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.

Thursday, April 29, 2010

biomathcraft **

Hyperbolic Crochet Snail or Seashell

The model is crocheted in half treble, 1 ply wool, starting with one stitch and increasing according to the series F(n) = 2F(n-2) + F(n-3), as given here.
Rows alternate, so that the increasing stitches are at the beginning of each row.

This creates a classic hyperbolic shape. It is interesting to see that the beginning and the end are in close to each other

To make up the model, fold in half. It configures neatly into a left hand or right hand spiral. Most shells in nature are right hand spirals.


Continue sewing the two sides together of the last row, while softly padding the spiral with wool fleece or cotton wool as you go.


Fibonacci Series

F1 .............0
F2 .............1
F3 .............1
F4 .............2 =(2x1) +0
F5 .............3 =(2x1) +1
F6 .............5 =(2x2) +1
F7 .............8 =(2x3) +2
F8 ...........13 =(2x5) +3
F9 ...........21 =(2x8) +5
F10 ........34 =(2x13) +8
F12 ........89 =(2x34) +21
F13 .......144 =(2x55) +34
F14 .......233 =(2x89) +55
F15 .......377 =(2x144) +89
F16 .......610 =(2x233) +144
F17 .......987 =(2x377)+233
F18 .....1597 =(2x610) +377


This series holds true forever along the Fibonacci series. As you can see, there are series within series.
.....................................................................
The sum total
F1 + F2+…….Fn = F(n+2) minus 1
This is useful to figure how many stitches are made from one skein of cotton or wool, and to plan accordingly how much material is need to complete a shape, various colours.
eg. F1 + F2+… F13 =376 =F15 minus 1.
One skein made 13 rows, that is 376 stitches.
.....................................................................
I am guessing that a hyperbolic shape is one which begins with one point and continues on in an orderly fashion until it becomes a fan shape with an exceedingly frilled edge. The definition of hyperbola in Wikipedia is hard for me to get my brain around.

One can also knit this shape but it needs to be started at the outer edge, eg 233 or 377 or even 610 stitches or more , so long as it fits on the knitting needles and follows the Pattern as in photo .

Hyperbolic Crochet Snail **

Hyperbolic Crochet Snail or Seashell

The model is crocheted in half treble, 1 ply wool, starting with one stitch and increasing according to the series F(n) = 2F(n-2) + F(n-3), as given here.
Rows alternate, so that the increasing stitches are at the beginning of each row.

This creates a classic hyperbolic shape. It is interesting to see that the beginning and the end are in close to each other

To make up the model, fold in half. It configures neatly into a left hand or right hand spiral. Most shells in nature are right hand spirals.


Continue sewing the two sides together of the last row, while softly padding the spiral with wool fleece or cotton wool as you go.


Fibonacci Series

F1 0
F2 1
F3 1
F4 2 =2x1 +0
F5 3 =2x1 +1
F6 5 =2x2 +1
F7 8 =2x3 +2
F8 13 =2x5 +3
F9 21 =2x8 +5
F10 34 =2x13 +8
F12 89 =2x34 +21
F13 144 =2x55 +34
F14 233 =2x89 +55
F15 377 =2x144 +89
F16 610 =2x233 +144
F17 987 =2x377+233
F18 1597 =2x610 +377


This series holds true forever along the Fibonacci series. As you can see, there are series within series.

The sum total
F1 + F2+…….Fn = F(n+2) minus 1
This is useful to figure how many stitches are made from one skein of cotton or wool, and to plan accordingly how much material is need to complete a shape, various colours.
eg. F1 + F2+… F13 =376 =F15 minus 1.
One skein made 13 rows, that is 376 stitches.

Tuesday, March 30, 2010

How to Create Models from Nature **


Hello and Welcome

Crocheting the hyperbolic space has become popular, thanks to Mathematician Dr Daina Taimina of Cornell University, and Margaret Wertheim from the Institute of Figuring http://www.theiff.org/

In the days to come I'd like to share the discoveries I have made for myself in crocheting the Fibonacci Series and other Mathematical series. I am just a beginner with digital camera and blogs. My email is tmvanam@gmail.com and I am glad of any ideas folk may have.

Cheerio from Tiiu V