Achievement Unlocked: Use the Fibonacci Sequence to Verify ID to Complete a Purchase

Achievement Unlocked: Use the Fibonacci sequence instead of an ID card to verify my identity and complete a purchase.

This evening, I found a nice practical real-world application of the Fibonacci sequence: I was buying a game (called "Pix") at Game Empire and was paying by credit card. The guy behind the counter asked to see an ID card, but I didn't have any with me. After I mentioned that the only thing I could do was to go back to my hotel room to get an ID, he decided that if I could correctly define the Fibonacci sequence that that would suffice instead of an ID card. So I gave him the correct definition, and we finished up the purchase.

(His idea came from the fact that I was using a Caltech Credit Union credit card. He wanted to make sure that card was legitimately mine. OK, I now have a nice story to tell --- which I appreciate --- but the logic was somewhat flawed. I did tell the guy that we both get an "Achievement Unlocked" for this.)

So don't ever let anyone tell you that there aren't any practical applications for the Fibonacci sequence!

Update: As Ernie Barreto points out, doing a Taylor-series approximation correctly was once a matter of life-or-death for physicist Igor Tamm. I am going to use that story when I teach Taylor series to my students.