The Fibonacci numbers and converting miles to kilometers

Courtesy of Mararie
This is an INTERESTING application of Fibonacci numbers!

Fibonacci numbers are the sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. (Add two numbers in the sequence to get the next one.)

Take two neighboring numbers in the sequence, such as 5 and 8. Turns out, 5 miles is approximately 8 km.  Take 34 and 55:  34 miles is about 55 km.

If your number is not in the sequence, write it as a sum of numbers that are:

Convert 10 miles into kilometers. 10 = 5 + 5, and 5 miles is about 8 km. So, 10 miles is about 16 km.

OR

Convert 25 kilometers into miles. 25 = 21 + 2 + 2.

21 km = 13 miles (about)
2 km = 1 mile (about)
2 km = 1 mile (about)


25 km = about 13 + 1 + 1 miles = about 15 miles.

More details here: Adventures in Fibonacci Numbers

The reason has to do with the fact that the conversion factor, (0.621371192 mi/km) is pretty close to the ratio to which sequential Fibonacci numbers converge (0.61803).

Comments

rational and irrational numbers said…
Rational numbers are (by definition) numbers that can be written as fractions. Since you can write any decimal as a fraction with a power-of-ten denominator, all finite decimals are rational.
Repeating decimals like 1.33333333... are also rational, by the way.
3:09 AM, July 20, 2012
John said…
Love it!
9:15 AM, July 30, 2012
Alex | Perfecting Dad said…
Hah, neat coincidence! As a Canadian I am often converting miles to kilometers.
3:42 PM, July 31, 2012
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