Fibonacci fibs and facts

(23 Feb. 2018) On the palm, two sets of spirals can be identified: the yellow ones turning to the right, and the blue ones spiraling to the left. At closer look there are five different spirals turning left, and 8 going to the right. Similarly, the pine cone has 5 spirals turning clockwise, and eight anticlockwise.
Also notice that the little flower on top has five petals.
5, 8 and 13 are some of the numbers that are called Fibonacci numbers. In this unique series the next number in the series is the sum of the last two numbers. The series starts with 0, 1, 1, 2, 3, and then…. 2+3 = 5: 0,1,1,2,3,5,…. and then 3+5=8 etc.
0,1,1,2,3,5,8,13,21,24,55,89 etc.
Two things are remarkable with these numbers.
The first is that many things in nature use these numbers. You may find flowers with four or twelve petals, but it is very unlikely. Most flowers have a number of petals corresponding to a Fibonacci number. Similarly, natural objects with spiraling elements like palm trees, pine cones, bunya pine cones, pine apples or sunflowers, normally have a number of spirals identical to a number of Fibonacci, for instance 3, 5, 8 or 13.
The second Fibonacci fact is a bit harder and is the basis of a lot of fibs and fiction regarding Fibonacci.
The spiral at the right is famous. This so called ‘Golden Spiral’ is drawn by using squares with sides the lengths of consecutive Fibonacci numbers: 1,1,2,3,5,8,13. In very delicate natural objects these spirals can indeed be identified, all be it very rarely. The fib and fiction kicks in when it is drawn like in this photo of a parrot. If the parrot looks up, then there is no sign of the spiral anymore: that is because the shape of the parrot has nothing to do with this spiral. In truth, spiral galaxies and nautilus shells, both often mentioned as examples of ‘Fibonacci, exhibit logarithmic spiral growth, but at a variety of angles usually distinctly different from that of the golden spiral.
Finding real Fibonacci features in nature is a great hobby. But it requires a good sense of what this sequence encompasses: and that has nothing to do with a parrot head. Don’t believe anything on web-pages “explaining” Fibonacci and the Golden section in two paragraphs or two pictures: trusting those sources is similar to accepting any truth in astrology or the healing power of snake oil.
You need to understand the math to really appreciate Fibonacci and the golden Section. Lucky me: I love math.