8/13/2019 Convert From Miles to Kilometers and Vice Versa Using Fibonacci Numbers and Sequences

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Convert from Miles to Kilometers and vice versa using Fibonacci Numbers and Sequences!!

byAbhash KumarinMBA Entrance Hacks20 August '13

Fibonacci numbers or Fibonacci series or Fibonacci sequence, named after Leonardo Fibonacci,

are the numbers in the following sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55....

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

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the relation

Fn = Fn-1 + Fn-2

with initial values Fo =0 and F1= 1

Here is how we can use this for our unit conversions from Miles to Kilometres.

Take two consecutive Fibonacci numbers, for example 8 and 13. Done. No seriously- there are13 kilometers in 8 miles. To convert back, just go the other way - 8 miles in 13 km!

Fibonacci numbers 34 and 55. We can conclude that there are approximately 55 km in 34 miles

and vice versa. (The exact answer is 54.7177 km.)

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8/13/2019 Convert From Miles to Kilometers and Vice Versa Using Fibonacci Numbers and Sequences

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What if you want to convert a value which is not a Fibonacci number? Well, you just need to

express this number as a sum of 2 or more Fibonacci numbers; individually convert them, and

add them up.

How many kilometers are there in 81 miles? 81 is not a Fibonacci number. But, we can express

81 as the sum of Fibonacci numbers (55+21+5). 89 is the Fibonacci number following 55, theFibonacci number following 21 is 34 and the Fibonacci number following that follows 5 is 8.

Therefore the answer is 89+34+8 = 131 kilometers in 81 miles. This is less than 1% off from the

precise answer 130.357km.

How many miles in 100 km? 100 is 89+8+3. Since we are going the opposite way now from

miles to km, we need the preceding Fibonacci numbers. 55, 5 and 2. Therefore, there are55+5+2= 62 miles in 100 km. The exact answer is 62.1371 miles.

Remember: To convert from km to miles, find the preceding Fibonacci number. But, to

convert from miles to km, find the subsequent Fibonacci number.

If the distance you're converting can be expressed as a single Fibonacci number, then fornumbers greater than 21 the error is always around 0.5%.

Here's why it works.

Fibonacci numbers have a property that the ratio of two consecutive numbers tends to theGoldenratioas numbers get bigger and bigger. The Golden ratio is a number and it happens to be

approximately 1.618.

Coincidentally, there are 1.609 kilometers in a mile, which is within 0.5% of the Golden ratio.

Now, if we take two consecutive Fibonacci numbers, Fn+1 and Fn, we know that their ratioFn+1/Fn is approximately 1.618. Since the ratio is also almost the same as kilometers per mile,

we can write Fn+1/Fn = [mile]/[km]. It follows that Fn[mile] = Fn+1[km]

That is all the elegance that there is to this concept. Almost a pure coincidence that the Golden

ratio is almost the same as kilometers in a mile.

http://mathworld.wolfram.com/GoldenRatio.htmlhttp://mathworld.wolfram.com/GoldenRatio.htmlhttp://mathworld.wolfram.com/GoldenRatio.htmlhttp://mathworld.wolfram.com/GoldenRatio.htmlhttp://mathworld.wolfram.com/GoldenRatio.htmlhttp://mathworld.wolfram.com/GoldenRatio.html