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Count the spirals in a sunflower and you find 21, 34, 55… Why does a flower know these numbers?
Fibonacci Spiral lab · Last updated: 16 October 2026
Count the spirals in a sunflower and you find 21, 34, 55 and so on. Why does a flower know these numbers? In this 3D lab, you grow a seed head one seed at a time and see the spirals appear. It reveals a beautiful link between a simple number pattern and the way plants grow.
What you'll discover
- In the Fibonacci sequence, each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21 and so on.
- Placing each new seed at the same golden angle from the last packs the seeds tightly with no gaps.
- That packing rule makes spirals whose counts are neighbouring Fibonacci numbers.
The science in plain words
The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, with each number made by adding the two before it. It was described in Europe by the mathematician Leonardo of Pisa, known as Fibonacci, in 1202, although Indian scholars had studied the same sequence centuries earlier in poetry and rhythm. As the numbers grow, the ratio of each to the one before gets closer and closer to about 1.618, the golden ratio.
A sunflower does not count anything. Its seeds form one at a time at the centre of the head, and each new seed appears at a fixed angle around from the previous one, about 137.5 degrees, called the golden angle. This angle is linked to the golden ratio, and it is very hard to approximate with simple fractions, so the seeds never line up in straight rows. Instead they fill the space evenly with almost no gaps, which packs in as many seeds as possible.
Look at the finished head and your eye picks out spiral arms curving clockwise and anticlockwise. Because of the golden angle, the numbers of these spirals are usually neighbouring Fibonacci numbers, such as 34 and 55. The same pattern shows up in pine cones, pineapples and the scales of some cacti.
Where it fits
- India, NCERT: A maths pattern beyond the NCERT science syllabus for classes 6 to 10.
- United States: Grades 6 to 8
Common questions
What is the Fibonacci sequence?
The Fibonacci sequence is a list of numbers where each one is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. It appears in nature, art and mathematics, and the ratio of neighbouring numbers approaches the golden ratio, about 1.618.
Why do sunflowers have Fibonacci spirals?
Each new seed grows at about 137.5 degrees round from the last one. This golden angle spreads the seeds evenly and packs them without gaps. That arrangement naturally forms spirals, and the numbers of spirals in each direction usually turn out to be neighbouring Fibonacci numbers.
What is the golden ratio?
The golden ratio is a special number, about 1.618, that appears when you divide a Fibonacci number by the one before it, as the numbers grow larger. It has unusual mathematical properties and turns up in geometry, in the arrangement of leaves and seeds, and in some art and design.
Related labs
- Fractals: One simple rule, repeated, grows a whole tree. How many twigs does it make, and how much space does it fill?
- Probability: Each bounce is a coin toss. Why do a hundred balls always pile up into the same shape?
- Population Dynamics: One plant becomes two, two become four… Can a population keep doubling for ever?
See all maths labs or every Taz science lab.
Try it yourself
The Fibonacci Spiral lab is one of the interactive 3D science labs inside Taz. Change one thing, predict what will happen, then run it and watch. Labs open after you sign in.