Distances and the Fibonacci Sequence


The Fibonacci Sequence is made up of numbers that are the sum of the previous two numbers in the sequence, starting with 0 and 1.

It goes like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, et cetera.

Observe how 1 equals 0+1; whereas 2 equals 1+1; 3 is 1+12; 5 is 2+3; and 8 is 3+5; and so on. The number after 144 is 233, or 89+144.

The Fibonacci number describes the golden spiral, an ideal form much beloved by artists, architects and designers through the ages. Interestingly, it also neatly matches the relationship between kilometers and miles.

Observe that three miles is roughly five kilometers, five miles is roughly eight kilometers, eight miles is roughly 13 kilometers. It’s not absolutely perfect because eight miles is actually 12.875 kilometers, but as top-off-the-head conversions go, it is immensely accurate.

“Thus the metric system did not really catch on in the States, unless you count the increasing popularity of the nine-millimeter bullet.”
– Dave Barry

If you need to convert a number that’s not on the Fibonacci sequence, you can just break out the Fibonacci numbers, convert, and add the answers. For instance, 100 can be broken down into 89 + 8 + 3, all Fibonacci numbers. The next numbers are 144, 13, and 5, which add up to 162. Note that 100 miles is actually equal to 160.934. Again, close enough.

2 thoughts on “Distances and the Fibonacci Sequence

  1. Small error: Observe how 1 equals 0+1; whereas 2 equals 1+1; 3 is 1+12; 5 is 2+3; and 8 is 3+5; and so on. The number after 144 is 233, or 89+144.

    Should be: Observe how 1 equals 0+1; whereas 2 equals 1+1; 3 is 1+2; 5 is 2+3; and 8 is 3+5; and so on. The number after 144 is 233, or 89+144.

  2. “Thus the metric system did not really catch on in the States, unless you count the increasing popularity of the nine-millimeter bullet.”
    – Dave Barry –

    Let’s not forget the two-liter soda bottle and the 1.75 liter liquor bottle, which, combined in a tall glass with ice and a good cigar, are subjects of great interest to me.

    The Fibonacci number describes the golden spiral, an ideal form much beloved by artists, architects and designers through the ages.

    The Fibonacci Sequence generates the Golden Ratio, a relationship so special it has even been called “the Divine Proportion.” The ratio of the successive Fibonacci Numbers gets closer and closer to a certain value as n gets larger and larger. The value it settles down to as n approaches infinity, is called by the Greek letter Phi or φ, and this number, known as the Golden Ratio, is approximately 1:1.61803399.

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