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Monday, November 24, 2014

The Fibonacci Spiral AKA The Golden Spiral In Sunflowers

[Update 12-10-14: Just found this amazing youtube vid expressing the beauty of these numbers.  It feels like it belongs in this post :)]

Vid Credit:Math on Youtube

My girlfriend and I took these pictures of gorgeous sunflowers near Lurray Caverns in VA.

Image Credits: my girlfriend and I.  And the sunflower gets a bit of credit too.  And math... gonna give math a bit of credit for once.

The Fibonacci Spiral, aka the "Golden Spiral," 
is a mirrored duplication rotated around the center to create the 
pattern found in sunflowers. 
Image:Wikimedia Commons-freely usable

Above, you see the Fibonacci Spiral: an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.

And to illustrate proportions within, here's a tiling with squares whose side lengths are successive Fibonacci numbers.
Image:Wikimedia Commons-freely usable

Fibonacci wasssss...?
...a math guru around 1200CE(AD) born right near the leaning tower of Pisa.  His efforts helped proved the Pythagorean Theorem (obviously pretty useful,) but he also offered the world some illumination on the topic of spiral patterns found in nature.[1] WHICH IS FASCINATING on top of being absolutely beautiful; and he's a lucky bugger to have his name forever connected to this.  Math found by nature... gotta love it.
[1 cite:]

Want to learn more on Fibonacci Numbers?  Let Me Google That For You :)

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