If you have never heard of this crazy number… you better check out this website (click on the title to get to it). The other day in my discrete math class we were talking about these things called generating functions, which sound kind of complicated, but they are just ways of expressing a list of numbers. A special list of numbers (a sequence) is the Fibonacci sequence. If you start with 1,1 then the next term is obtained by adding them together; so 2. Then the next term is obtained by adding 2 and 1; so 3. You repeat this to get an infinite sequence of numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,…
Well.. this seemingly simple sequence has a generating function with the golden ratio inside it! In fact if you take the numbers way out in the sequence (the really big ones, like 610 and 987) and divide the bigger one by the smaller one, the proportion approaches the golden ratio. And the golden ratio is an irrational number! Even cooler than that… it appears everywhere: architecture, geometry, music, nature. Here is an awesome quote from the wikipedia article:
Adolf Zeising, whose main interests were mathematics and philosophy, found the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors. In these phenomena he saw the golden ratio operating as a universal law.
In 2003, Volkmar Weiss and Harald Weiss analyzed psychometric data and theoretical considerations and concluded that the golden ratio underlies the clock cycle of brain waves.[51] In 2008 this was empirically confirmed by a group of neurobiologists.[52]
In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.[53]
Several researchers have proposed connections between the golden ratio and human genome DNA.
Anyways… I think all this stuff is really cool and it really blew my mind this past week. I think it shows so clearly the beauty of mathematics, God and His creation.
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