GC2BQAY Leonardo Fibonacci and the Golden Ratio (Traditional Cache) in South Carolina, United States created by IkeHurley13

This cache has been archived.

Ike 13: I have a new can ready to go (it's not the same, but it will do). But I do not plan on putting it anywhere near these trails. Hopefully a new listing will be out before too long. Thanks to all who hunted!

GC2BQAY ▼

A cache by IkeHurley13 Message this owner

Hidden : 7/18/2010

Difficulty:

Terrain:

Size: Size: regular (regular)

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Geocache Description:

This is the nineteenth cache in my finite mathematical series. I am a math teacher by day. I thought a cache series dedicated to math would be a good way to educate the public.

Fibonacci has many names: Leonardo Pisano Bogollo, Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, and Leonardo Fibonacci. In 1202 he examined a simple question, and found an amazing pattern.

The problem, "Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was... How many pairs will there be in one year?"

The result is known as the Fibonacci sequence. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.... Notice each term is added to the previous term to find the next term in the sequence. So after 1 full year there would be 144 pairs of rabbits!

Even more amazing is the link this sequence has to an ancient ratio that had not every been truly defined. Set up a fraction of two consecutive terms of the Fibonacci sequence, as you go higher into the sequence that fraction will approach what we know call the Golden Ratio. The Golden Ratio is 1: 1.618 or .0618 to 1. This ratio was used back in the time of ancient Greeks, and symbolized perfection and beauty. The more you study the Golden Ratio, the more amazing it is. Notice the reciprocals (the two decimal numbers above are reciprocals) have a difference of 1. This is the ONLY example of reciprocals having a difference of 1.

The most amazing fact about the Fibonacci numbers and the Golden Ratio is how often they come up in nature. Check out the related web page to see all the examples.

You will be looking for the Golden Ammo Can that celebrates my first 1000 cache finds. The ammo can sadly does not have a Golden Ratio, but is stuffed with swag. Please trade up or even. The cache is located off the Quail Valley Trail System. There is a large amount of wildlife in the area, so watch your step.

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