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Fibonacci and friends *March 2, 2007*

*Posted by eric22222 in General, Math.*

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Truly, 11 PM is the greatest time for shopping. Always easy to get a parking spot, no crowded aisles, and no lines at the register. Basically, no *people*.

Before I get rolling, I’d like to point out a cool new feature underway from the fine folks at Google: Google Reader. If you have lots of blogging friends (as I do), this tool allows you to automatically see any updates without having to check every blog for changes. When you go to a site you want to subscribe to, look at the right side of the URL bar (for Firefox users, at least). Click on the orange icon (RSS feed) and follow step by step instructions. Now you’re reading blogs in style!

Today, I acquired Skill: Balloon animal: Teddy bear. Don’t ask how. It’s pretty crazy.

Our CS140 class today centered around functions that activate themselves while they’re being run. Eventually, this got to the Fibonacci Sequence. That, for some reason, got me pretty excited. I guess I’m just a fan of numbers: their patterns, quirks, and amazing relationships. The Fibonacci Sequence is a set of numbers. The first is 0, the second is 1, and the rest are the sum of the two before it. It goes like: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, etc.

Anyway, the series shows up in flowers’ seed patterns, seashells, and all sorts of stuff. You know those right triangles that are easy to remember? Like a 3-4-5, or 5-12-13? Starting with 5, every other number in the sequence is the largest of a set of Pythagorean Triples. As the sequence approaches ∞, a number in the sequence divided by the one before it approaches the golden ratio, also a really cool concept found all over the place

I’m not really going anywhere with this besides saying that I like numbers. The end.

The golden ratio is one solution to the perfect packing problem (i.e. how to perfectly pack a group of different size objects into a set space). That’s one reason why seashells and flowers seem to exhibit it so often. A flower that can pack more seeds into a small area, or a gastropod that can fit more of its body into its shell, is likely to be more successful than others who have to increase their size to hold the same amount of stuff.

Neat, huh?

Evolution and math rock my world…. :p

[…] ’til. I got out my notes and began jotting some numbers down. First one, then another one, then two, three, five, eight, thirteen… […]