Counting on it

Among my hobbies, I include mathematics. I know, you're thinking, "what a dork".

Many people can do math, but fewer understand it, and even fewer enjoy doing it. I'm one of the ones that do. No, I don't sit around and contemplate the meaning of "four", but if I see an article about a new largest prime number or minimal surface, I'm gonna read it. I consider textbooks on differential equations to be "light reading". I stare at fractals. I own a slide rule, and I can use it. I can entertain myself by deriving an algebraic formula for the Fibonacci sequence.

Fibonacci seqeunce? I'm glad you asked! Suppose you have some rabbits that grow from babies to breeding adults in one day, always give birth to one male and one female each day, and never die.

• On Day 1, you start with one pair of baby rabbits (male and female).
  
• On Day 2, you have one pair of adult rabbits.
  
• On Day 3, you have 2 pairs: the adult pair and a baby pair.
  
• On Day 4, you have 3 pairs: the original adult pair, the new adult pair, and another baby pair.
  
• On Day 5, there are 5 pairs: three adult pairs and two new baby pairs.

And so on, and so on.

This is the Fibonacci sequence: the first term is 1, the second term is 1, and every term after that is the sum of the previous two terms. So, F(1)=1, F(2)=1, F(3)=1+1=2, F(4)=1+2=3, F(5)=2+3=5, and so on, and so on.

Now you're thinking, "he's a dork with a rabbit fetish".

Anyway, the point, such as it is, is that as we as a society rely more and more on calculators and spreadsheets to do our math for us, the less we care about the theory behind it and the less able we are to teach it to the next generation, which is a vicious locus of points in a plane that are equidistant from a given point, er, circle. The other day I saw a news article (well, a Yahoo news article) that said that some math teachers are as little as just one chapter ahead of their students, and I'm not terribly surprised.

I stop at Sonic for two sausage breakfast burritos nearly every morning. It costs $3.88. One day all I had was a ten-dollar bill and some change, and not wanting to use a credit card for such a small purchase, I thought, I'll give the person $10.13 and I'll get back six dollars and a quarter, no problem. The carhop could not process this bit of mathematic manipulation, and instead proceeded to give me back the 13 cents and then give me 6.12 change from the ten.

After this, I looked more closely at the receipt, and printed right on there is "CTND .12". That's "change to next dollar, 12 cents". Really. Apparently, some people need a slip of paper to tell them that 3.88 from 4 is 12 cents. Now, I always pay for my breakfast with a credit card, and I don't feel awkward about it.

In case you're wondering, F(n) = (((1+√5)/2)ⁿ-((1-√5)/2))ⁿ)/(2√5).

Hassenpfeffer, anyone?