It was a common lament of high school to hear about mathematics: "How does this apply to the real world?". This was often echoed by people with little patience or imagination. Fear not, math lovers. A more mature understanding of math is that it is used EVERYWHERE in the real world.

Every single thing you own depends on math. Whether it's your sneakers or your iPod, everything you own required someone to know mathematical concepts to create those objects. The more complex the object, the more mathematics, science, and engineering knowledge it requires to produce it.

There is no magic here, however. Anyone can begin to understand these concepts by reading web sites and observing nature. The Da Vinci Code book and movie made the Fibonacci Sequence come into fame, but people have long known about the curious relationship of the PHI ratio to rest of the cosmos and its natural order.

You can read all about the Fibonacci Sequence on Wikipedia and elsewhere on the web. Here are some of the best links I have found about it.

http://en.wikipedia.org/wiki/Fibonacci_number (Thanks to my uncle Kevin, of http://www.CompuMagic.com, for reminding me of this tonight
http://www.beautyanalysis.com/ (Ever wonder exactly why someone like Natalie Portman looks so beautiful? It's in her PHI. Beauty is in the PHI of the beholder. Watch this web site's presentation to understand how it works!)
http://goldennumber.net/
http://www.goldenmuseum.com/
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html
http://www.cs.wfu.edu/~burg/papers/DancingWithFractals.pdf
http://www.dchaos.com/spiral.html

Something you may not know is that Google Calculator will spit out the Golden Ratio if you just type "phi" as your search term: http://www.google.com/search?q=phi&start=0&ie=utf-8&oe=utf-8&client=firefox-a&rls=org.mozilla:en-US:official

To summarize the Golden Ratio, just follow this simple sequence:

0,1,1,2,3,5,8,21,34,55,89,144,233,377,610,987,1597

Now, if you divide successive terms the average approaches the decimal 1.618

**What is so amazing about that? Everything. It's simple and pervasive in nature.**

How does it apply to different fields of study?

Horticulture:
The proportion of PHI appears all over in plants in their natural growth patterns. It's also used in designing visually appealing gardens.
Graphic Design:
The Fibonacci Sequence is a fundamental concept for creating visually appealin graphics of well-balanced proportions.
Human Anatonmy:
The human body exhibits very logical PHI-proportions. In fact, plastic surgeons use "Golden Ratio masks" to exhibit the "perfect face". You can see all about this on this web site: http://goldennumber.net/face.htm
Computer Programming:
Computer science courses use computing the Fibonacci sequence as an exercise in recursive programming. It is also involved in fractals.
Another interesting application is Fibonacci math applied to dance performance:
http://www.cs.wfu.edu/~burg/papers/DancingWithFractals.pdf

Returning to the 1.618 ratio and the golden sequence, when you elect to plot these ratios on paper, you get a shape like this:

This looks suspiciously like a shell's growth pattern:

It's also similar to the growth pattern of spiral galaxies and hurricanes!

So, math and patterns like this are everywhere! Studying the universe leads to discoveries like this that make it both comprehensible and mysterious.

You can also see the Fibonacci Sequence growth pattern in the proportions of the human body:

And in the beautiful facial proportions of Natalie Portman:

Or, if you're a woman reading this, perhaps George Clooney is more your style?

Maybe you had Frosted Flakes for breakfast and like tigers:

Or in the proportions of your fingers:

Maybe you like famous artwork, but couldn't quite pinpoint what makes it seem so beautiful:

While I have not seen any evidence of "The Golden Ratio" in ordinary popular dances, there was a specific effort to employ math and dance at Wake Forest University. Read all about it here in "Dancing With Fractals":

http://www.cs.wfu.edu/~burg/papers/DancingWithFractals.pdf

I have observed the beauty of many dance patterns, and the most exciting parts are always the turns and spins, as evidenced by the following videos:

Magna Gopal spinning dozens of times: