# Definition:Fibonacci Number/Historical Note

## Historical Note on Fibonacci Numbers

Leonardo Fibonacci famously discussed this sequence in his *Liber Abaci*, in the context of breeding pairs of rabbits.

Hence the name **Fibonacci numbers**, which was given to this sequence by François Édouard Anatole Lucas, who studied them in detail.

The sequence $\sequence {F_n}$ was known to Indian mathematicians as long ago as the $7$th century C.E.

It was also studied by Gopala before $1135$, and by Acharya Hemachandra in about $1150$.

Hence some sources refer to these numbers as the **Gopala-Hemachandra numbers**.

They are also discussed by Johannes Kepler in his work of $1611$ *De Nive Sexangula* (*On the Six-Cornered Snowflake*). It is suspected that Kepler was himself unfamiliar with Fibonacci's work.

Kepler himself had noticed the appearance of Fibonacci numbers in the growth of plants:

*It is in the likeness of this self-developing series that the faculty of propagation is, in my opinion, formed; and so in a flower the authentic flag of this faculty is shown, the pentagon. I pass over all the other arguments that a delightful rumination could adduce in proof of this.*

## Sources

- 1919: Leonard Eugene Dickson:
*History of the Theory of Numbers: Volume $\text { I }$*: Chapter $17$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $5$ - 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): Liber Abaci: $88$ - 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $5$ - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Fibonacci sequence**(Fibonacci, 1202) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Fibonacci sequence**(Fibonacci, 1202) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $4$: Lure of the Unknown: Cubic equations