# Fibonacci Formula

## Fibonacci Formula

Leonardo Pisano Bogollo, an Italian, discovered the Fibonacci Formula first. The Fibonacci Formula is a series of whole numbers that goes as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,… This is an endless formula that begins with 0 and 1 and ends with the sum of the two terms before it. Study materials are available on Extramarks for students to learn more about this topic.

The Fibonacci Formula is  Fn = Fn – 1 + Fn – 2. The Fibonacci Formula is made up of infinite terms such as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,… In basic words, it is a series in which each number is the sum of the two numbers before it is in the formula. Its first and second terms are 0 and 1. Fibonacci numbers are the terms of this formula. It operates according to the rules of a closed-form expression. That is, it is defined by a linear recurrence with constant coefficients. The ratio between the Fibonacci numbers converges as the formula of numbers continues. They get quite near to the Golden Ratio as they progress, but it is not an exact match.

This notion has various applications, both in Mathematics and in nature. For example, the Fibonacci Formula may be used to explain the sums of Pascal’s Triangle’s shallow diagonals. It may also be used to count compositions with {1, 2 } restrictions. The formula is also important in determining the computing run-time of Euclid’s method. The Fibonacci Formula may be found in nature in the fruits of a pineapple, the blossoming pattern of an artichoke, the unfurling process of a fern, the arrangement of a pine cone, and the family tree of a honeybee. Many flowers exhibit this principle in their blossoming structure as well.

Applications of Fibonacci Formula are numerous. There are countless additional occurrences of the Fibonacci Formula in the real world aside from these uses of the Fibonacci Formula in Mathematics and nature.

• Finance

The Fibonacci Formula appears multiple times in the worlds of finance and economics. The Fibonacci retracement is a stock market trading analysis tool that describes a phenomenon in which stock values fluctuate predictably. Brock-economic Mirman’s growth model incorporates the notion as well.

• Music

Composer Joseph Schillinger used the Fibonacci Formula as applied to melodies to construct works, with the intervals between notes defined by the formula. Schillinger’s works differ from Golden Ratio music, which takes a similar notion in a different direction.

• Miles to Kilometres Conversion

The Fibonacci Formula may be used to acquire a broad sense of miles over longer distances since the conversion factor from miles to kilometres is extremely near to the Golden Ratio.