This unusual shaped afghan is based on the Golden Mean and the Fibonacci Sequence.
The shape is known as the Golden Spiral.
The Golden Mean is a special ratio which has been used widely, around the world, for thousands of years, in art and design. It also occurs very often in nature. Items using these proportions ‘look right’ to most people.
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Worked in one piece, entirely in crochet trebles (UK definition).
The spiral is really a series of connected quarter-circles.
The Golden Spiral can be made with any type of yarn. The original was made with DK yarn. Using a thicker, or thinner, yarn would make the piece larger, or smaller.
It is possible to add extra sections, or omit some sections. Any such modifications will change the size by a substantial amount.
The pattern also contains several variations for more complex use of spirals.
The design uses two different mathematical ideas: the Golden Mean and Fibonacci Numbers.
The Golden Mean has many other names. The Ancient Greeks described it as ‘dividing a line in the extreme and mean ratio’. Renaissance artists called it ‘Divine Proportion’.
This special ratio has been used widely, throughout the world, for thousands of years in art and design. It may have been used for constructing the Pyramids in Egypt.
It also occurs very often in nature. Items using these proportions ‘look right’ to most people. Maybe it is because it occurs so often in nature that man-made items using the same proportions are so appealing to us. Even credit cards are in the shape of the Golden Rectangle!
The Golden Mean is often represented by the Greek letter Phi. It is an irrational number, which means that the decimal places never end. It is calculated to be 1.6180339887 ...
In knitting and crochet, where you can’t work with part stitches, it is near enough to say that each measurement is about 1.6 times longer than the one before.
A Golden Spiral is often shown as a series of quarter circles joined together. This depiction is not quite accurate. The instructions in this pattern use this less accurate method but, due to the flexible nature of crochet, this is insignificant. It is based on the Fibonacci sequence of numbers.
The Fibonacci Sequence is well known. It is derived by adding consecutive numbers to give the next in the series.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ...
The spiral is derived from quarter circles using those numbers, in sequence, as the radius of the circle.
As the sequence progresses the relationship between the numbers tends towards to Phi. This means that the further you go in the sequence the closer to Phi the relationship becomes.
Mathematically, the sequence could go on for ever. The afghan stops at 89.
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Adding the border means that the proportions of the completed afghan are not quite those of the Golden Mean. If you want to maintain mathematical accuracy you can omit the border or mount the spiral on a rectangle of fabric or crochet, as described in the instructions.
The photo and progress reports were sent by Carla:
Finally finished!!!!!! Took forever, or at least seemed that way!! Another wonderful pattern from Wooly Thoughts!!!! I think I’ll stick to their knit patterns…. crochet just isn’t my thing any more!! LOL!!
It’s now in the washer with a pair of jeans on hot….. felt here we come!!!!
It’s out of the washer and pinned out on my blocking boards!! One small problem…. my Blueberry didn’t felt as hard as the Lavender!! It gives it a tiny ruffle on the edge….. which is really cute!!! It ended up being 59” X 28.5” after felting!!!