# Kilometers to Miles Conversion — Approximation of Fibonacci Series

Fibonacci — an infinite series of numbers in which every subsequent number is the sum of two preceding numbers.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, …

There are many real-life applications of Fibonacci Numbers. Among these applications one is the conversion of Kilometers to Miles.

Select any two adjacent numbers from the series e.g. 8 and 13. Assuming smaller number is in miles & larger number is in kilometers.

8 Miles = 13 Kilometers (According to the Fibonacci series)

Let’s verify it by miles to kilometer formula,

1 Miles = 1.60934 Kilometer

8 Miles = 8 * 1.60934 = 12.8747 Km ≈ 13 Km

Shocked ????

Let’s again take random two consecutive numbers e.g. 34 and 55 & now convert from kilometers to miles.

55 Kilometers = 34 Miles

1 Km = 0.621371 Miles

55 Km = 55 * 0.621371 = 34.17540 ≈ 34 Miles

To calculate the distance of those numbers which are not part of the Fibonacci numbers i.e. 9, we can split that number into two or more Fibonacci numbers.

For instance, to convert the 9 Miles into Kilometer we can proceed as follows,

9 Miles = 8 Miles + 1 Miles (or) 5 Miles + 2 Miles + 2 Miles

8 Miles → 13 Km

1 Miles → 2 Km

9 Miles = 13 km + 2 km = 15 km (approximately)

The main REASON is how it works ?

The general formula of calculating the Fibonacci Number is,

F(n) = 1.618*F(n-1)

Where the constant value 1.618 is called Golden Ratio (φ), which is the ratio of the circumference of a circle to its diameter.

Or we can calculate this Golden ratio value by using different techniques of Numerical Method i-e perform the specific operation repeatedly and at some point the values converge up to three decimal places (3dp).

Similarly, the formula of converting the Miles to Kilometers is,

1 Miles = 1.60934 kilometers

which is approximately same to the Golden Ratio. That’s the reason Fibonacci Series is used as the conversion scale of Miles to Kilometers.

Richard A. Dunlap — “It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms.”

The Man of Numbers — Italian Mathematician, Leonardo Pisano Bogollo (1170–1250) was a founder of Fibonacci numbers, lived in Pisa, Italy. His nickname was “Fibonacci” which means “Son of Bonacci”. He was also famous to introduced the Hindu-Arabic Numbers (0,1,2,3,4,5,6,7,8,9) in Europe in place of Roman Numbers (I, II, III, IV, V, etc).

Every year, mathematicians are celebrating Fibonacci Day on November 23rd because the date is written in the mm/dd format (11/23) as it has the digits “1, 1, 2, 3” which is part of the sequence.

Written by