Fibonacci numbers were Sanskrit prosody tools before Fibonacci
Each Fibonacci number is the sum of the previous two, giving 0, 1, 1, 2, 3, 5, 8, 13, and so on. Indian scholars such as Pingala described them by about 200 BC while counting poetic syllables; Leonardo of Pisa's name stuck centuries later in Europe.
The sequence listed as A000045 in the OEIS supports a journal, the Fibonacci Quarterly, and turns up in the Fibonacci search technique, the Fibonacci heap and Fibonacci cubes for linking parallel systems, and ties to the golden ratio via Binet's formula—consecutive ratios approach that constant. The recurrence extends to negative indices with a sign relation linking negative-index terms to positive ones.
Sanskrit prosody asked how many patterns of long and short syllables fill a line; Pingala's cryptic phrase about mixing the two is read as early Fibonacci recurrence, with clearer statements later from Virahanka as quoted by Gopala. European popularization followed Fibonacci's rabbit puzzle centuries afterward. Bharata Muni's writings also show awareness of the pattern.
Hemachandra, around 1150, also wrote that the next meter count comes from adding the last two. Leonardo of Pisa brought the numbers to Western Europe in his 1202 Liber Abaci, using an idealized and biologically unrealistic rabbit farm: one newborn pair in a field becomes two pairs after two months, three after three and five after four, because each month's total adds last month's pairs to the mature pairs from two months back. The label Fibonacci sequence came only in the nineteenth century, from the number theorist Édouard Lucas, whose own Lucas numbers obey the same recurrence. Binet's closed formula carries the name of Jacques Philippe Marie Binet, although Abraham de Moivre and Daniel Bernoulli already knew it.
Source: Fibonacci sequence
