Has anyone ever heard of the Fibonacci Numbers? They are a sequence of numbers that follow a fairly simple pattern.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... and so on.
Figure out the pattern yet?
If you haven't, here's the spoiler: each number in this sequence is the sum of the 2 previous numbers. (0+1=1, 1+1=2, 1+2=3, 3+2=5 etc.)
Sounds pretty simple right? Well what if I told that this pattern of numbers may be the most important sequence of numbers ever discovered? What if I told you that this sequence of numbers holds the key to understanding the mathematical processes of our natural world? What if I told you that the Fibonacci
Numbers appear in nature more frequently than any other pattern of numbers? Would you be curious?
The fact is, Fibonacci numbers ARE found in nature quite frequently. Perhaps what is most prevalent is the ratio of these numbers...
If we take the ratio of two successive numbers in Fibonacci's series, (1, 1, 2, 3, 5, 8, 13, ..) and we divide each by the number before it, we will find the following series of numbers:
1/1 = 1, 2/1 = 2, 3/2 = 1·5, 5/3 = 1·666..., 8/5 = 1·6, 13/8 = 1·625, 21/13 = 1·61538...It seems that as we continue along this pattern, we seem to be narrowing down to one specific number. That number is known as "Phi" - but in numerical terms it is about 1.618033.
This ratio we are referring to is also known as the "Golden Ratio" and can be found almost everywhere in nature!
Try Googling "Golden Ratio" or "Fibonacci Numbers." Report back with some interesting photos and/or natural patterns you have found.
Extra credit - What is the relationship between this photo below and the Fibonacci Numbers? (E-mail me the answer to this question, or hand in a hard copy in class.)
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