By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument.

Using the Fibonacci sequence would keep the number of grains within any one field at minimum.

In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence:

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.

In mathematical terms, the sequence F < sub > n </ sub > of Fibonacci numbers is defined by the recurrence relation

A page of Fibonacci's Liber Abaci from the National Central Library ( Florence ) | Biblioteca Nazionale di Firenze showing ( in box on right ) the Fibonacci sequence with the position in the sequence labeled in Roman numerals and the value in Hindu-Arabic numerals.

The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody.

Susantha Goonatilake writes that the development of the Fibonacci sequence " is attributed in part to Pingala ( 200 BC ), later being associated with Virahanka ( c. 700 AD ), Gopāla ( c. 1135 ), and Hemachandra ( c. 1150 )".

* Implementation to calculate Fibonacci sequence in Lisp

In 2008, Alexander guest-starred on the CBS show Criminal Minds in the season four episode " Masterpiece " as Prof. Rothschild, a well-educated serial killer obsessed with the Fibonacci sequence who sends the team into a race against time to save his last victims.

To illustrate how one may use Newton's formula in actual practice, consider the first few terms of the Fibonacci sequence f = 2, 2, 4 ... One can find a polynomial that reproduces these values, by first computing a difference table, and then substituting the differences which correspond to x < sub > 0 </ sub > ( underlined ) into the formula as follows,

These are based on a generalisation of the Fibonacci sequence.

The Fibonacci sequence may be described by the recurrence relation:

In mathematics, several specific infinite sequences of bits have been studied for their mathematical properties ; these include the Baum – Sweet sequence, Ehrenfeucht – Mycielski sequence, Fibonacci word, Kolakoski sequence, regular paperfolding sequence, Rudin – Shapiro sequence, and Thue – Morse sequence.

Fibonacci numbers is the basic example of a problem in enumerative combinatorics.

In the Sanskrit oral tradition, there was much emphasis on how long ( L ) syllables mix with the short ( S ), and counting the different patterns of L and S within a given fixed length results in the Fibonacci numbers ; the number of patterns that are m short syllables long is the Fibonacci number F < sub > m + 1 </ sub >.

* Leonardo Fibonacci writes Liber Abaci, about the modus Indorum, the numbering method of India ; it is the first major work in Europe toward moving away from the use of Roman numerals.

The year 610 is a Fibonacci number.

It is also a Fibonacci number, a happy number, and one of only 3 known Wilson primes.

A Lagged Fibonacci generator ( LFG ) is an example of a pseudorandom number generator.

The implementation based on a min-priority queue implemented by a Fibonacci heap and running in is due to.

He is the discoverer of several graph algorithms, including Tarjan's off-line least common ancestors algorithm, and co-inventor of both splay trees and Fibonacci heaps.

In mathematics, Fibonacci coding is a universal code which encodes positive integers into binary code words.

where F ( i ) is the ith Fibonacci number.

For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, … ( the Fibonacci sequence ) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description.

Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of ( decimal ) digits of b. He also proved a special case of Fermat's last theorem.

The fruit of a pineapple is arranged in two interlocking helices, eight in one direction, thirteen in the other, each being a Fibonacci number.

Generally, each floret is oriented toward the next by approximately the golden angle, 137. 5 °, producing a pattern of interconnecting spirals, where the number of left spirals and the number of right spirals are successive Fibonacci numbers.

The angle 137. 5 ° is related to the golden ratio ( 55 / 144 of a circular angle, where 55 and 144 are Fibonacci numbers ) and gives a close packing of florets.

Liber Abaci ( 1202, also spelled as Liber Abbaci ) is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci.

Another example in this chapter, describing the growth of a population of rabbits, was the origin of the Fibonacci sequence for which the author is most famous today.

# Where we generally write a fraction to the right of the whole number to which it is added, Fibonacci would write the same fraction to the left.

That is, we write 7 / 3 as, while Fibonacci would write the same number as.

The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas ( 1842 – 1891 ), who studied both that sequence and the closely related Fibonacci numbers.

In 1999, Divakar Viswanath showed that the growth rate of the random Fibonacci sequence is equal to 1. 1319882487943 …, a mathematical constant that was later named Viswanath's constant.

* List of topics named after Fibonacci

Pisano periods are named after Leonardo Pisano, better known as Fibonacci.

Zeckendorf's theorem, named after Belgian mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers.

There also exists a class of quasiperiodic superlattices named after Fibonacci.

* Binet's formula for the Fibonacci sequence is named after Jacques Binet.

The school also places every student in one of four houses named after an outstanding person in the fields of mathematics, physics, biology and chemistry: Fibonacci, Faraday, Fleming and Nobel respectively.

He is also recognized as the first to describe the rule for multiplying matrices in 1812, and Binet's formula expressing Fibonacci numbers in closed form is named in his honour, although the same result was known to Abraham de Moivre a century earlier.