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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.

 


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Re: Happy Phi Day!
Sean Kinney  Account Info

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


Re: Re: Happy Phi Day!
O4saken1  Account Info

hey, what do all those stand for (the MYTI89 is obvious)

     18 June 2000, 14:36 GMT

Re: Re: Re: Happy Phi Day!
ColdFusion

Fibbonaci
Oppenheimer
Hawking (stephen)
Entropy


     18 June 2000, 15:40 GMT


Re: Re: Re: Happy Phi Day!
Hecatomb  Account Info
(Web Page)

HAWKNG (HAWKING)
OPNHMR (OPEN HUMOR)

And please tell me what irrational number Psi is. I have been trying to figure this out for a while and I haven't come to any conclusion what-so-ever.

     18 June 2000, 15:43 GMT

Psi equals...
Grant Elliott  Account Info
(Web Page)

Phi=(1+sqrt(5))/2
Psi=(1-sqrt(5))/2=1-Phi

     18 June 2000, 17:36 GMT


Re: Psi equals...
EvanMath

In addition:
Phi - 1 = Psi
1/Phi = Psi (and, of course, 1/Psi = Phi)

     18 June 2000, 20:33 GMT


Re: Re: Psi equals...
Grant Elliott  Account Info
(Web Page)

um... Neither of those statements was true. Check your math.

     18 June 2000, 20:36 GMT


Re: Re: Re: Psi equals...
Dave Stroup  Account Info
(Web Page)

Actually those statements are true.
Phi - 1 == 1/Phi == Psi

Its an interesting characteristic of Phi.

     18 June 2000, 20:56 GMT


Re: Re: Re: Re: Psi equals...
Grant Elliott  Account Info
(Web Page)

Actually:
1/Phi = Phi-1 = -Psi
So the two posts ago should have been:
Phi-1 = -Psi
1/Phi = -Psi

Don't forget Psi is negative...

     19 June 2000, 00:31 GMT


Re: Re: Re: Re: Re: Psi equals...
mysteryegg  Account Info
(Web Page)

1/phi = phi-1 is an interesting start for calculating phi... we tried it in sixth grade... mathcounts was a very special time (don't bother pointing out that mathcounts is only for 7th/8th graders)

     19 June 2000, 01:30 GMT

Re: Re: Re: Re: Re: Re: Psi equals...
SigmaPhi  Account Info

umm....mathcounts is only for 7th/8th graders

Hardy Har Har......

     20 June 2000, 00:31 GMT


Mathcounts
Ryan Castellucci  Account Info

I rember being on the mathcounts team. we got first place in the chapter, i myself got fourth indviule. my school actualy had two teame both of witch placed. we won 5 of the 8 trophies.

_\ / |)
|otta|)yte

     20 June 2000, 21:03 GMT


Re: Re: Re: Re: Re: Re: Psi equals...
nolekid  Account Info

I don't care if this 2001, but our team got like 20th. I got 5th. too bad I didn't make state.

     22 March 2002, 22:03 GMT


Re: Re: Re: Re: Happy Phi Day!
JaggedFlame

Not Open Humor, Oppenheimer.

     19 June 2000, 18:15 GMT

More Useless Number Theory
Grant Elliott  Account Info
(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=(1-sqrt(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 = (N-1)/1

Rearanging gives us:

0=N^2-N-1

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: More Useless Number Theory
Clovis_Sangrail  Account Info

Ooh boy! I sure do love math now, Mr. Narrator!

---Very good Donald.

Quack Quack!

     18 June 2000, 19:45 GMT


Re: More Useless Number Theory
YesMan  Account Info

I haven't seen that movie in years!!! Does anyone know if I can rent it or buy it?

     19 June 2000, 06:43 GMT


Re: Re: More Useless Number Theory
Chris Moultrie  Account Info
(Web Page)

Donald in Mathamagic land...yes...itz still available.

     20 June 2000, 01:42 GMT


Re: Re: Re: More Useless Number Theory
techfury  Account Info

Oh jeez, I saw it in school like a month ago. Pretty good video.

     24 June 2003, 02:19 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  Account Info
(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

Re: Re: Happy Phi Day!
Nick Disabato  Account Info
(Web Page)

And e day is February 78th.

Please look at a calendar and tell me if a February 78th exists. ;)

--BlueCalx

     19 June 2000, 00:43 GMT

Re: Re: Re: Happy Phi Day!
The_Professor  Account Info
(Web Page)

Actually, using that logic, e day would be February 71, not 78 - e ~
2.718281828459045235360287471352 66249775724709369995957496696762 77240766303535475945713821785251 66427427466391932003059921817413...

     19 June 2000, 06:00 GMT


Re: Re: Re: Happy Phi Day!
Chris Moultrie  Account Info
(Web Page)

Maybe just February 7th?

     20 June 2000, 01:44 GMT

Re: Re: Happy Phi Day!
mysteryegg  Account Info
(Web Page)

we'll just pretend it's 1/phi day... or -psi day :P

     19 June 2000, 01:32 GMT


Re: Re: Happy Phi Day!
Daniel Bishop  Account Info
(Web Page)

It probably has something to do with the fact that 3/14 and 6/18 exist but 1/41 and 1/61 do not.

Another question: Why is Mole Day October 23 (10^23)instead of June 2 (6.02)? I think it's because, in June, students are too focused on the end of the school year to care about a mathematical constant day.

     20 June 2000, 19:51 GMT

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