Spirals, seeds and the Fibonacci numbers

Start with 1 and 1. Add them to get 2. Keep adding the last two numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. This is the Fibonacci sequence, named after an Italian mathematician who wrote about it around 800 years ago. Mathematicians in India had described the same numbers even earlier.

Spirals in seed heads

Look closely at a sunflower head and you will see the seeds packed in spirals, some curving clockwise and some anticlockwise. Count the spirals in each direction and you often get two neighbouring Fibonacci numbers, such as 34 and 55. Pine cones often show 8 and 13, and pineapples 8 and 13 as well.

Why would a plant do that?

A growing tip makes new seeds or scales one at a time, each turned a fixed angle from the last, about 137.5°. That angle spreads them out so they don't line up in rows and leave gaps. Packing seeds this way fits the most seeds into the space, and the spirals, with their Fibonacci counts, appear as a side effect.

Other patterns in nature

Be a careful scientist

Not every pine cone or sunflower gives Fibonacci numbers. Some give other counts, and people sometimes only report the ones that fit. That makes this a great claim to test yourself: collect pine cones from different trees, count the spirals both ways, record every result, and work out what percentage fit the pattern.