playing with numbers

For someone who studied the sciences my mathematics is terrible.

So I was reading a story the other day and I read about the Fibonacci Series. Once it’s explained, it’s so easy – it’s a series of numbers where the next number is the sum of the previous two, so it goes:

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597

The origin for the series date back to 1202 when Fibonacci was thinking about the reproductive rate of rabbits. Really? Really.

It’s possible to find Fibonacci numbers without going through the addition, for instance to find f(500) involves a lot of adding so some guy called Binet worked out the formula for that. There’s also another formula to find the next term in the series.

Now, relating to the Fibonacci series is the golden number, which denotes the ratio between the long side and the short side of the most aesthetically pleasing rectangle. The definition of a golden rectangle is one that, when squared, gives another golden rectangle. For an illustration, go here.

The golden number has been denominated by the greek letter phi (φ) and has been calculated to be 1.61803398875…

So how do the Fibonacci series and the golden number relate. Watch. First take the first few Fibonacci numbers:

f(1) = 1
f(2) = 1
f(3) = 2
f(4) = 3
f(5) = 5
f(6) = 8
f(7) = 13
f(8) = 21
f(9) = 34
f(10)= 55

Then divide each number by the one before it:

r(1) = 1/1 = 1
r(2) = 2/1 = 2
r(3) = 3/2 = 1.5
r(4) = 5/3 = 1.6666..
r(5) = 8/5 = 1.6
r(6) = 13/8 = 1.625
r(7) = 21/13 = 1.6153846
r(8) = 34/21 = 1.6190476
r(9) = 55/34 = 1.6176471
r(10)= 89/55 = 1.6181818

Essentially the further we go in this calculation the closer we get to φ. Neat isn’t it.

What’s that got to do with real life? Not surprisingly there’s so much of mathematics in nature. Many flowers have a Fibonacci number of petals, like sunflowers have 34 petals and daisies 34, 55 or 89.

I wished I was better at all this. It’s quite fascinating.