The golden section

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat2.html

 

“2.1 Why is the Golden section the “best” number?

“The links in this section are to Quicktime animations. They are worth viewing as they show the dynamics of what might happen if seeds were not placed with a phi-angle between them.

Why not 0·6 of a turn per seed or 0·5 or 0·48 or 1·6 or some other number?

First we can agree that turning 0·6 of a turn is exactly the same as turning 1·6 turns or 2·6 turns or even 12·6 turns because the position of the point looks the same. So we can ignore the whole number part of a turn and only examine the fractional part.

Also, since a 0·6 of a turn in one direction is the same as 0·4 of a turn in the other, we could limit our investigation to turns which are less than 0·5 too. However sometimes it will be easier to talk of fractions of a turn which are bigger than 0·5 or even that are bigger than 1, but the only important part of the number is the fractional part.

So, in terms of seeds – which develop into fruit – what is a fruit-ful numbers? Which has the best properties as a turning angle for our meristem? It turns out that numbers which are simple fractions are not good choices, as we…..”

 

 

 

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About Katherine

I like poetry and history
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