What is the Fibonacci sequence?

The Fibonacci sequence is an infinite series of integers where each number is the sum of the two preceding ones, typically starting with 0 and 1. First described in Indian mathematics and later introduced to Western Europe by Leonardo of Pisa, these numbers appear widely in computer algorithms, mathematics, and natural settings like plants. They also maintain a deep connection to the golden ratio and Lucas numbers.

What we know

• The Fibonacci sequence is an integer series where each element is the sum of the two elements that precede it, starting with 0 and 1. [1, 2, 4]
• The sequence was first described in Indian mathematics as early as 200 BC in work by Pingala on Sanskrit poetry patterns. [2]
• Leonardo of Pisa, also known as Fibonacci, introduced the sequence to Western European mathematics in his 1202 book Liber Abaci. [2]
• Fibonacci numbers appear in biological settings such as tree branching, leaf arrangements, pine cones, artichokes, and pineapples. [2]

Where to go next

• whoWho was Leonardo of Pisa?
• compared withHow do Lucas numbers relate to Fibonacci numbers?
• the bigger pictureWhat is the golden ratio?
• the bigger pictureWhat are integer sequences?
• a case in pointWhat is a Fibonacci word?
• an unexpected connectionHow does Sanskrit poetry relate to mathematical sequences?Early descriptions of the Fibonacci sequence originated from studying syllable patterns in ancient Sanskrit poetry.

Sources

• [1]Fibonacci sequence (Wikidata Q23835349) · CC0 1.0
• [2]Fibonacci sequence · CC BY-SA 4.0
• [3]Fibonacci word · CC BY-SA 4.0
• [4]Integer sequence · CC BY-SA 4.0
• [5]Complete sequence · CC BY-SA 4.0