This morning's science/maths video takes a look at something that has always fascinated me and inspires some of my nature photography: capturing the Fibonacci series in plants.
The Fibonacci series was named for the 13th century Italian mathematician, Leonardo Pisano, whose popular nickname was Fibonacci. As a child, Fibonacci studied maths with Arabs and later published the book, Liber Abaci.
Besides being famous for introducing Europeans to the superiority of the Hindu-Arabic numeral system over the Roman numeral system, Fibonacci also discovered popularised a simple numerical series that is the foundation for an incredible mathematical relationship with phi. This series of numbers is described by this recurrence relation:
Fn=Fn-1 + Fn-2 where F0=0 and F1=1, &tc.
or we could write it this way:
0+1=1
1+1=2
1+2=3
2+3=5
.
.
.
That formula describes the series of numbers that starts out thus:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
The Fibonacci series can then be used to draw a series of blocks next to each other whose sizes are consistent with the numerical ratios described by the Fibonacci series, like this:
Then, if we then draw a line from one corner to the opposite corner of each block, we end up with a spiral that looks like this -- a spiral that looks very similar to the chambered nautilus pictured at the top:
As you can see, the Fibonacci Series is deceptively simple, but its ramifications and applications are complex, subtle and nearly limitless. This mathematical relationship is commonly seen in nature. In plants, for example, it is visible in the numbers of leaves and petals, spirals in flowers and in their seed heads, and in the sections in fruits. It is part of the explanation why four-leafed clovers are vanishingly rare, for example.
This fun and fascinating video explains this further:
Visit Vihart's YouTube channel [video link]
.. .. .. .. .. .. .. .. .. .. .. ..
twitter: @GrrlScientist
facebook: grrlscientist
evil google+: grrlscientist
email: grrlscientist@gmail.com
