Wednesday, August 12, 2009

... and you've lost your tape measure again!

Did you ever think about the Golden Ratio ... and how does it relate to knitting? (go on - you do!) Artists, designers, painters, plastic surgeons, mathematicians all know about the Golden Ratio. It is said that the pyramids were built using this ratio. And now Knitters are in the game too!

Simply put, the distance from one portion of your body to another is in direct proportion to another. For example: measure the width of your mouth at rest, then measure the width of your nose, the ratio on an attractive face will be...1.618. All the ratios on your body will be ... 1.618. If you were ... perfect. Mine are 1.4287. I'm not so perfect.

Leonardo da Vinci's drawings of the human body emphasised its proportion. The ratio of the following distances is the Golden Ratio: (foot to navel) : (navel to head). Get it?

However, did old Leo ever know that the distance from the tip of your thumb to the first joint is approximately 1"? Did he realize that the distance from your palm to the tip of your center finger is approximately 4"? Did he see that the span of your hand, with the fingers spread very wide, from the tip of your thumb to the tip of your center finger is approximately 7"? Huh? Did he? This is very handy when knitting socks.
Why to tell you this? How many times have you been caught without your tape measure? See? ... just a little bit of knowledge ... and just in case you wanted to take this further ...

The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …

The closed-form expression (known as Binet's formula, even though it was already known by Abraham de Moivre) for the Fibonacci sequence involves the golden ratio:

F\left(n\right)   = {{\varphi^n-(1-\varphi)^n} \over {\sqrt 5}}   = {{\varphi^n-(-\varphi)^{-n}} \over {\sqrt 5}}\,.

Disclaimer: Of course, inner beauty is more important than external beauty... yeah, and i'm a six foot blond with a swan-like neck and a voice like Barbra Streisand!


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