Who?, I hear you cry! Well stop chattering at the back of the class and pay attention and I'll explain.
Leonardo Bonacci (1170- c. 1245 and known as Fibonacci) was an Italian mathematician who invented the Fibonacci Series, in which each term is the sum of the preceeding two.
The series starts 1 1 2 3 5 8 13 21 and on it goes.
As you get further into the sequence, the ratio between adjacent terms becomes a very good approximation to the Golden Ration (known as Phi), which is also related to the Golden Angle.
This series and the Golden Angle are found to govern the spacing of many things in nature, one particularly good example of which is the pattern of seeds in a sunflower head (which is all to do with getting the tightest spacing of seeds).
Sunflower by John Liddle, on Flickr
You can clearly see the spiral spacing of the seeds.
It is possible to produce a plot of this pattern (see https://timwolverson.wordpress.com/2...iral-in-excel/ ) using Excel.
As part of her botanical studies, SWMBO is writing a dissertation on Fibonacci and so did the calculations and produced a plot mimicking the sunflower seed pattern.
Spiral2 (Large) by John Liddle, on Flickr
I repeated the exercise and fiddled with the number of points produced to try and get it to overlay with the sunflower head, but it proved too difficult.
However, we also had an image of a pine cone, the scales of which exhibit the same sort of spiral pattern, but in rather smaller in numbers.
After a bit of experimentation, I arrived at the image below - each scale (apart from small natural variations|) coincides with one of the Fibonacci dots.
Large Pine Cone with spiral by John Liddle, on Flickr
Amazing!
Leonardo Bonacci (1170- c. 1245 and known as Fibonacci) was an Italian mathematician who invented the Fibonacci Series, in which each term is the sum of the preceeding two.
The series starts 1 1 2 3 5 8 13 21 and on it goes.
As you get further into the sequence, the ratio between adjacent terms becomes a very good approximation to the Golden Ration (known as Phi), which is also related to the Golden Angle.
This series and the Golden Angle are found to govern the spacing of many things in nature, one particularly good example of which is the pattern of seeds in a sunflower head (which is all to do with getting the tightest spacing of seeds).
Sunflower by John Liddle, on FlickrYou can clearly see the spiral spacing of the seeds.
It is possible to produce a plot of this pattern (see https://timwolverson.wordpress.com/2...iral-in-excel/ ) using Excel.
As part of her botanical studies, SWMBO is writing a dissertation on Fibonacci and so did the calculations and produced a plot mimicking the sunflower seed pattern.
Spiral2 (Large) by John Liddle, on FlickrI repeated the exercise and fiddled with the number of points produced to try and get it to overlay with the sunflower head, but it proved too difficult.
However, we also had an image of a pine cone, the scales of which exhibit the same sort of spiral pattern, but in rather smaller in numbers.
After a bit of experimentation, I arrived at the image below - each scale (apart from small natural variations|) coincides with one of the Fibonacci dots.
Large Pine Cone with spiral by John Liddle, on FlickrAmazing!
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