## A Fibonacci day

On Facebook, Sally Byers reminds me that  today is a Fibonacci day: an M/D/Y (in US notation) in which M + D = Y (5/8/13: 5 + 8 = 13) and M and D are successive Fibonacci numbers (starting from the pair of integers 1, 1). This is the fifth Fibonacci day in this century — 1/1/02, 1/2/03, 2/3/05, 3/5/08, and now 5/8/13. It’s also the penultimate Fibonacci day in this century: 8/13/21 will be the last, and then no more (since there’s no 13th month).

More days: triangular days, in which M, D, and Y are successive triangular numbers: in this century, 1/3/06, 3/6/10, 6/10/15, 10/15/21, and then we run out.

And square days, in which M, D, and Y are successive square numbers: 1/4/09, 4/9/16, 9/16/25, and again we run out.

And cubic days, in which M, D, and Y are successive cubic numbers: 1/8/27, 8/27/64, and that’s the end.

Meanwhile, there are arithmetic days, in which the differences between M versus D and D versus Y are constant. A lot of these, for instance 11/12/13 (difference of 1), 9/11/13 (difference of 2), 7/10/13 (difference of 3), 5/9/13 (difference of 4).

And geometric days, in which the ratios between M over D and D over Y are constant — as in 3/6/12 (ratio of 2), 2/6/18 (ratio of 3), 1/4/16 (ratio of 4).

And exponential days, in which the exponents of M on D and D on Y are constant (D = M^x and Y = D^x): for instance, 2/4/16 (exponent of 2), 3/9/81 (exponent of 2).

So today (5/8/13) is a Fibonacci day and tomorrow (5/9/13) is an arithmetic day. Lots of special.

### 2 Responses to “A Fibonacci day”

1. strangeguitars Says:

For me this gives me two very strong opposite emotions. On one hand, I absolutely love the idea of having “Fibonacci days”, etc, but on the other, M/D/Y makes my skin crawl! It’s not enough to put the dates backwards so the small numbers are on the left (D/M/Y), no, it has to be worse than that! 😉

I’ll celebrate my Fibonacci day this year on August 5th!

• arnold zwicky Says:

You mean: on 5 August. 🙂