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Cross Curricular Maths

Fibonacci in nature

Look for spirals and patterns while avoiding overclaiming.

Quick answer

Fibonacci numbers are found in nature, like in the spiral patterns of sunflowers, pinecones, and nautilus shells. These numbers follow a special pattern where each number is the sum of the two before it.

Learning outcome

By the end of this page, you will be able to spot Fibonacci patterns in nature and understand how these numbers are made. Success signs:
  • You can count the spirals in a pinecone or sunflower.
  • You can explain how Fibonacci numbers are made (add the two previous numbers).
  • You can find examples of Fibonacci in your home or garden.

Why this matters

Fibonacci numbers help us understand how nature builds itself. They show up in flower petals, seashells, and even the shape of galaxies. Learning about them helps you see the maths all around you and makes you more curious about how things grow and change.

How it works

Fibonacci numbers start with 0 and 1. Then, each number after that is the sum of the two numbers before it. Here’s how it works step by step:
  1. Start with 0 and 1
  2. 0 + 1 = 1
  3. 1 + 1 = 2
  4. 1 + 2 = 3
  5. 2 + 3 = 5
  6. 3 + 5 = 8
  7. 5 + 8 = 13
  8. 8 + 13 = 21
  9. 13 + 21 = 34
  10. 21 + 34 = 55
  11. 34 + 55 = 89
  12. 55 + 89 = 144
You can keep going forever. This pattern shows up in nature because it helps plants and animals grow in the most efficient way.

Examples you can see

Let’s look at some real-life examples of Fibonacci numbers in nature: Sunflowers: If you look closely at a sunflower, you can see spirals going in two directions. The number of spirals in each direction often follows Fibonacci numbers like 34 and 55. Pinecones: Pinecones have scales that form spirals. Count the spirals going up and down – you’ll often find 5 and 8 or 8 and 13. Nautilus shells: The spiral shape of a nautilus shell grows larger with each turn. The way it expands matches the Fibonacci pattern. Flower petals: Many flowers have petals in Fibonacci numbers. Lilies have 3 petals, buttercups have 5, and daisies often have 21 or 34 petals. Tree branches: If you look at how tree branches grow, the pattern often follows Fibonacci numbers. Each branch splits into two, then those split again, and so on. You can even try making your own Fibonacci spiral with a pencil and paper. Start with a square that is 1 unit wide. Then add a square of 1 unit, then 2 units, then 3 units, then 5 units, and so on. Connect the corners to make a spiral.

Try it as a mini adventure

Adventure: The Fibonacci Hunt You are a nature detective on a mission to find Fibonacci numbers in your garden or around your home. 1st time: Look at a flower. Count how many petals it has. 2nd time: Look at a pinecone. Count the spirals going up and down. 3rd time: Look at a sunflower. Count the spirals in the middle. 4th time: Draw a Fibonacci spiral using squares. 5th time: Check if the number of spirals or petals matches a Fibonacci number. Can you find more than 3 examples of Fibonacci numbers in nature today?

Common mistakes

  • Mistake: Thinking that all numbers in nature follow Fibonacci. Why it happens: People get excited and see patterns everywhere. Fix: Remember that not everything is Fibonacci, but many things are. Look closely and count carefully.
  • Mistake: Counting petals or spirals wrong. Why it happens: It’s easy to miscount, especially with small numbers. Fix: Count slowly and double-check. Use your fingers or small objects to help.
  • Mistake: Thinking that Fibonacci numbers are just for math class. Why it happens: Math can seem separate from the world. Fix: Realise that nature uses math to build itself. Fibonacci numbers are part of the world’s design.

Parent and carer guide

Parents and carers can help by:
  • Going on a nature walk and looking for flowers, pinecones, or shells together.
  • Using the Fibonacci spiral activity to draw and explore.
  • Encouraging children to count and talk about what they see.
  • Not worrying if the child doesn’t get all the numbers right. The focus is on curiosity and observation.
  • Using simple language and real examples to explain the idea.
This is a great time to show that math is all around us. Let your child explore and ask questions. Don’t correct every mistake – instead, help them discover and enjoy the fun of finding patterns in nature.

Practice questions

  1. What are the first 6 Fibonacci numbers?
  2. How many petals does a daisy usually have?
  3. What are the next two numbers after 8 and 13 in the Fibonacci sequence?
  4. Which of these numbers is NOT a Fibonacci number: 5, 8, 12, 21?
  5. How many spirals are usually in a pinecone?
Answers:
  1. 0, 1, 1, 2, 3, 5
  2. 21 or 34 petals
  3. 21 and 34
  4. 12
  5. 5 and 8 or 8 and 13

FAQ

What is the Fibonacci sequence?

The Fibonacci sequence is a series of numbers where each number is the sum of the two before it. It starts with 0 and 1.

Who discovered Fibonacci numbers?

The sequence was named after Leonardo Fibonacci, a 12th-century Italian mathematician who introduced it to Europe.

Are all numbers in nature Fibonacci?

No, but many things in nature follow the pattern. It’s a common way for nature to grow and build.

Why do Fibonacci numbers appear in nature?

They help plants and animals grow in the most efficient way. This allows them to use space and resources better.

Can I make my own Fibonacci spiral?

Yes! Start with a square of 1 unit, then add 1, 2, 3, 5, 8, and so on. Connect the corners to make a spiral.