Happy Phi Day!
Posted by Nick on 18 June 2000, 08:07 GMT
Today, June 18, is Phi Day. As Daniel Bishop pointed out, Phi is an irrational number, not unlike Pi. Approximately equal to 1.61803398874989484820458683436564 (today is June 18  6/18  har har har), Phi is used a great deal in astronomy. Most importantly, it's found in the proportions in the Greeks' famous golden rectangle. It's deriveable by many proofs, including the famous Fibonacci Sequence (one of my personal favorite series, if there even is such a thing). For more information on Phi, click here and here.



The comments below are written by ticalc.org visitors. Their views are not necessarily those of ticalc.org, and ticalc.org takes no responsibility for their content.


Re: Happy Phi Day!

Sean Kinney

Oh, and Nick. I intend to get the FBONAC license plate if no one else has taken it. Or how about OPNHMR for those of you with a nuclear fetish? I am partial to HAWKNG, though. ENTRPY might be equally good. And don't forget MYTI89. :P


18 June 2000, 10:27 GMT


More Useless Number Theory

Grant Elliott
(Web Page)

Oh, I just love these number days (although I'm still disappointed we didn't celebrate April 2nd...)! Now, it's time for more of, "Grant Babbles Meaninglessly About Useless Number Theory Somewhat Related to Today's Date." Joy!
Since no one has taken the opportunity to write a definition of phi and examples of it's many uses, I shall start with that:
Phi=(1+sqrt(5))/2=1.6180339887.....
This is very similar to Psi:
Psi=(1sqrt(5))/2=.6180339887
The best use (and in fact the original use) of phi is in the Golden Rectangle. For this reason, phi is commonly refered to as the Golden Ratio. A Golden Rectangle is a rectangle drawn with side lengths in the ration 1:N (N>1) such that removing a square (with side length equal to the length of the shorter side) from one side, the sides of the remaining rectangle are also in the ration 1:N. (That makes a lot more sense if you look at a picture.) Based on that definition, we obtain the following proportion:
1/N = (N1)/1
Rearanging gives us:
0=N^2N1
Which we solve to reveal that N equals (you guessed it) phi or psi. Since psi is negative, it is not a terribly practical side length for a rectangle. Hence, phi is the Golden Ratio.
What the heck does that prove? Quite a bit actually. The Greeks found that most of nature is somehow linked with the Golden Ratio. For example, the human body can be drawn nested in a series of Golden Rectangles. The face is an excellent example. Most Greek art displays this perfection. Renaissance artists revisited this classic ideal.
Furthurmore, spirals found in nature also display this ratio. Drawing lines tangent to the curve and perpendicular with each other results in a boxed off spiral. The line segments in this spiral are in the Golden Ratio. The best example of a "perfect" spiral in nature is a seashell. Spirals also have a connection to Fibbonacci, which I will get to later.
There are many more examples of this perfection in nature. Examples include branches on trees (Fractals!) and sunflowers (Fibbonacci!). I highly recommend seeing the movie, "Donald in Mathemagic Land." I know it sounds stupid, but it has a great deal of interesting information in it, including an excellent explanation of the Golden Ratio.
Back to spirals. Look at a sunflower. The seeds sprial outward rather than being in little nested circles. Better still, look at the seeds in each "level." There's 1, then 1, then 2, then 3, then 5...etc. Recognize it? Of course, Fibbonaci! Why this happens is fairly obvious if you look at the structure of the sunflower. It's hard to describe; I was serious when I said to go look at one.
It gets better, the sunflower's spiral is one of those "perfect" spirals. The Golden Ratio is in there too! Isn't math fun? It gets better still! (Oh, the excitement!) This is great! There's a formula relating Fibbonaci with phi and psi! How cool! Here it is. The Nth Fibbonaci number is equal to:
(phi^N  psi^N)/sqrt(5)
Oh, this is just too awesome! Aren't you having fun? Oh, admit it... You want more. Well, for now, this will have to be it. But I will write more in a reply to this message if I have time. Until then...
This has been another installment of, "Grant Babbles Meaninglessly About Useless Number Theory Somewhat Related to Today's Date." Thank you.


18 June 2000, 17:30 GMT


Re: Happy Phi Day!

JaggedFlame

All right! Phi Day's on my birthday! Cool!


18 June 2000, 21:00 GMT


Re: Happy Phi Day!

MathJMendl
(Web Page)

If phi is 1.61803398874989484820458683436564, shouldn't phi day be January 61st (1.61) instead of June 18th (618)? I mean, pi day (3.14159265358979323846264338327 9502884197169399375105820974944) is March 14th (3.14), not January 41st (141). Then again, maybe phi day should be January 6th. Oh well. This is all too arbitrary.


18 June 2000, 21:56 GMT


1 2 3
You can change the number of comments per page in Account Preferences.
