Today the date is 5-8-13! Those numbers are in the Fibonacci sequence, in order. And at 11:23 (am or pm), we will experience a very special moment in time: 1 1 2 3 5 8 13, the first seven numbers after 0 in the Fibonacci sequence. Unlike Pi Day, or Tau Day, this special Fibonacci minute will only be experienced today.
(To those of you reading this in the United States: unfortunately this doesn’t apply to you. Your Fibonacci day was celebrated earlier this year, on May 8.)
As many of you probably know, the Fibonacci sequence shows up in some unexpected places. For example, most pine cones have a Fibonacci number of spirals. So too does the sequence appear in pineapples, sunflowers, daises and broccoli.
If you measure the length of bones in your fingers, you’ll find a Fibonacci sequence. You can even use the Fibonacci numbers to convert miles to kilometres: 5 miles = 8 km, 8 miles = 13 km, etc.
Golden ratio, golden spirals
Now, hold on to your seats, we’re about to go deeper: if you look at the ratio of consecutive Fibonacci numbers, you’ll find that this ratio approaches the same number, which we call the golden ratio. So, 8 divided by 5 is an approximation of the golden ratio. Then, 13 divided by 8 is a better approximation, 21 divided by 13 is an even better approximation, etc. You can try this out for yourself, with larger and larger numbers in the sequence.
Then, you can make this ratio into a golden spiral, by making the spiral get wider (or further from its origin) by a factor of the golden ratio for every quarter turn it makes, which looks like this:
This golden spiral also appears in some uncanny places in nature – including when we look to space. Spiral galaxies, including our own galaxy the Milky Way follow the golden spiral pattern (see right) as the arms of the galaxy spread out from the centre.
Of course, all of this could just be a little mathematical coincidence, but it does show mathematics and nature at its most beautiful.
Happy Fibonacci Minute.
For the idea for this post, hat tip to Carrie Bengston and Michael Evans.