Wednesday, 1 October 2008

Fibonacci's Thumb

One of those things that goes around the internet math groups every now and then, is going around again.... things to do with the Fibonacci sequence. I call them Fibonacci Rules of thumb... Ok, you remember Fibonacci, he introduced the Arabic numbers to the west with his famous book, The Liber Abaci.. and had a problem about rabbits where the number each month was given by 1, 1, 2, 3, 5, 8, 13, 21, etc....... YEAH, the one in the DaVinci Code!

The most common Fibonacci Rule of Thumb is converting between miles and kilometers. Suppose you are zipping along in Canada and the speed limit is in Km/hr, and you wonder..."Gosh, just how fast AM I driving?". So take your speedometer reading in good old miles per hour, and think of the number in the fibonacci sequence nearest this one... suppose you are driving a modest 55 mph.. which just happens to be a number in the sequence. Find the next number in the sequence, in this case 89, and that is a really good estimate of your speed in Km/hr (OK, I think it works out to be more like 88.5, but you get the idea).

So why does that work? The typical conversion is miles = 1.609344 kilometers (I know, I just googled it); and if you take any Fibonacci number, and divide it by the one in front, you get about that number. As the numbers get larger and larger, the ratios get closer and closer to 1.618033989.... so the ratios are pretty close. Of course you could use it for lots of other things, and with a little torture, you can make it work for less usual measures... If you want to know how many seconds (appx) in N years, where N is a Fibonacci number, then you can just take the next Fibonacci number, double it, and multiply by 107... So for example, If you wanted to find the number of seconds in 5 years... the next Fibonacci number is 8... double that to get 16... and now add the seven zeros to get 160,000,000 seconds in five years. You can check that one on your own.

And if you are STILL not convinced, would you be impressed if I told you that for N electrons (where N is a Fibonacci number), you can find the charge in Couloumbs by taking the next Fibonacci number, and multiply by 10-19... NOW THAT IS USEFUL STUFF

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