Read in the Da Vinci Code that phi = 1.68

[jai6638]

Hey.. .i just read in the Da Vinci Code that phi = 1.68 and that everythin in thie universal has the same proportion.. and that its called the DIVINE Proportion... For example, if you divide the length between your head to ur toe by the length between your waist and toe ur going to get the value of phi, i.e. , 1.68..


Is this true?? In what context is phi used in mathematics or physics?

thanks

 

[rachmaninoff]

For example, if you divide the length between your head to ur toe by the length between your waist and toe ur going to get the value of phi, i.e. , 1.68..

Hmm, I got 1.53...

 

[Gokul43201]

Not "everything", definitely.

It's nice to say that there are all these mysterious properties attributed to phi, but that's mostly to keep you interested. There are some interesting things about the number phi, like the construction of rectangles within rectangles, and the limiting ratio of terms in a fibonacci sequence.

I really don't know of any real applications of phi in math or physics, nor do I suspect there would be any reason for it being particularly "appliable."

 

[SGT]

For a good analysis, look at:
http://www.straightdope.com/columns/040618.html

 

[HallsofIvy]

No, it is not true that "everythin in thie universal has the same proportionl" (and that is NOT said in "The DaVinci Code").

The "divide proportion" is connected to the "Golden Rectangle" which is mentioned in
"The DaVinci Code" (DaVinci's "Last Supper" is in the proportions of a golden rectangle): If you mark off a length on the longer length, equal to the width of the rectangle, you divide the rectangle into a square (the "width by width") and a rectangle (the remaining part). If the original rectangle is a "golden rectangle", then the new smaller rectangle will be also: in both the ratio of length to width is the same: the "divide proportion".

The calculation: Call the length of the original rectangle l and its width w. If we cut off a "w by w" square, we have left a rectangle with sides of length w and l-w. Now, w is the longer "length" so the ration of "length to width" is w/(l-w) which must be equal to the original l/w:
$$\frac{w}{l-w}= \frac{l}{w}$$

Multiplying by w(l-w) gives w²= l(l-w)= l²- lw.

If we divide both sides of that by w², we get
1= (l/w)²- (l/w). let x= l/w and we have 1= x²- x or
x²- x- 1= 0. Solving that by the quadratic formula,
$$x= \frac{1+\sqrt{5}}{2}$$
is the "divine ratio".

It's interesting but it is NOT "divine"!

 

[DaveC426913]

Um, 'Halls of Ivy' seems to have a cold. :) He keeps saying the "divide proportion".


The divine proportion is common in nature. Spiral seashells and other recursive structures exhibit properties based on it.

As far as the human body goes, that's nonsense. That is the trickery of numerology - you can always find numbers that fit your claim if you look hard enough, and are highly selective in your choices.

Someone once showed that the Statue of Liberty was of "obvious" extraterrestrial origin becasue its height in inches was exactly equal to the distance to Alpha Centauri minus the number of leap days since its construction - or some such silliness.

 

[SGT]

The divine proportion is common in nature. Spiral seashells and other recursive structures exhibit properties based on it.

For a debunking see:
http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm

 

[DaveC426913]

Huh. I am guilty of having a simplistic view of this subject. I had always assumed that the golden ratio was a generalized set of curves, and the nautilus was just in that range.

I'll have to give that page a careful looksee and reflect deeply.

(This comes at a bad time. I am reading Crichton's book 'State of Fear'. The story, while fiction, does to Global Warming what this site did to my views on magic numbers in nature. Makes me question some of my basic and long-held beliefs, particularly the ones rooted in common- or "everybody knows"-knowledge.)

 

[CeeAnne]

Wow. I really like HallsofIvy's response. I am so, like, very impressed. and I also like the "divide proportion". That is so very clever. Henceforth, I, too, shall refer to the "divide proportion". I love it! Thank you HallsofIvy. Hugs. -CeeAnne-

 

[Gokul43201]

Um, 'Halls of Ivy' seems to have a cold. :) He keeps saying the "divide proportion".

 

[wlvanbesien]

For the programmers amonst us:

	public double findPhi(int degree){
		double phi = 1.0;

		int n = 1;
		while ( n < degree + 1 ){
			phi = Math.sqrt( phi + 1 );
			n++;
		}
		return phi;
	}

This is some code I wrote a little while ago, in Java.

 

[Tide]

Actually, you can do it without resorting the square roots in your loop. Use:

$$\phi = 1 + \frac {1}{\phi}$$

 

[HallsofIvy]

AAAAAChooo!