﻿ Golden Spiral
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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. It is said that 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 a special way of dividing a line and 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. We used this less accurate method but, due to the flexible nature of crochet, this is insignificant. The afghan design 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: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ...

Our 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  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.

It took quite a few attempts to work out how yo make this in one piece, in a simple way. Surprisingly, it starts with the innermost point of the largest quadrant and adds on the smaller pieces as it goes along.

The disadvantage of this design is that there are gaps in the spiral so it needs to be supported by a backing to avoid holes where your feet might go straight through.

GOLDEN SPIRAL