What Is the Fibonacci Sequence? Numbers, Nature and History

Q: What is the Fibonacci sequence?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two numbers before it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. It’s named after Italian mathematician Leonardo of Pisa, known as Fibonacci, who introduced it to Europe in his book Liber Abaci in 1202.

How it works

Step	Calculation	Result
Start	—	0, 1
3rd number	0 + 1	1
4th	1 + 1	2
5th	1 + 2	3
6th	2 + 3	5
7th	3 + 5	8
8th	5 + 8	13

The rabbit puzzle

In Liber Abaci, Fibonacci asked how many pairs of rabbits there would be after a year if each pair produced a new pair every month, starting from their second month. The answer follows the sequence: 144 pairs after 12 months.

Indian mathematicians, including Pingala and later Virahanka, described the same numbers centuries earlier while studying patterns in Sanskrit poetry.

The golden ratio

Divide each Fibonacci number by the one before it, and the result gets closer and closer to about 1.618, known as the golden ratio (φ, phi):

8 ÷ 5 = 1.6
13 ÷ 8 = 1.625
89 ÷ 55 ≈ 1.618

Fibonacci in nature

Example	Where the numbers appear
Sunflowers	Seed spirals often come in counts like 34 and 55
Pinecones	Spirals in two directions, often 8 and 13
Flowers	Many have 3, 5 or 8 petals
Pineapples	Scales in 8, 13 and 21 spirals

These patterns help plants pack seeds and leaves efficiently. Not every claim about Fibonacci in nature holds up, though; the famous nautilus shell, for example, isn’t a true golden spiral.

Fibonacci’s bigger legacy

Liber Abaci also helped spread the Hindu-Arabic numerals (0–9) across Europe, replacing Roman numerals in trade and accounting, arguably a bigger contribution than the sequence itself.

Fibonacci Day

Some people celebrate November 23 (written 11/23 in the US) as Fibonacci Day.

For other famous number facts, see the only even prime number and what pi is.