Fibonacci

I think I'm enjoying learning about non-linear patterns a great deal because there are so many applications of this pattern in nature. Also, since I was in the sixth grade, I've always held an awe for anything relating to the Golden Section.

This last Christmas I actually knit a scarf for my brother that followed the sequence of stripping for the first several numbers in the sequence.

1,1,2,3,5,8,13,21....

When I was substitute teaching several years ago I had fifth grade class who was reviewing number patterns and sequencing... I put a number of different sequences up on the board. There was a student who was moderately autistic in the class and before I completed one of the sequences he blurted out "Fibonacci! Fibonacci!"

I spent some time fiddling and I built my own tiled visual model of the Fibonacci sequence. I think I spent too much time trying to make sure that the squares were positioned correctly. I truly feel that hands on manipulation of visuals is key to helping me grasp and understand concepts fully. I hate passive learning.



You can draw a spiral around the pattern of increases and it looks something like this.

A Fibonacci Spiral is similar to a "Golden Spiral" based on the Golden Ratio. However, if you try to apply the the Fibonacci design to a nautilus shell interior you see that the ratio of the growth increases do not fit.