Thread: is phi real?

I all the Da Vinci Code says about phi true?

Originally Posted by pendragon526

I all the Da Vinci Code says about phi true?

for those of us who havn't read or seen it...

what does it say about phi?

The Golden Ratio by Mario Livio is a good book to cut through all the new age hype surround phi and see where it is actually present and where it takes some real fudging to find it.

phe exists. it has the value of about 1,618
phy²=phi+1
1/phi=phi-1

Originally Posted by Zelos

phe exists. it has the value of about 1,618
phy²=phi+1
1/phi=phi-1

Actually phi = 0.5*( 1 + Sqrt(5) ), and no one here is doubting that a number called phi exists, just if it is as present in art and engineering as claimed by some quarters.

in some art it is, but it has most likly to do with the human minds ability to find what it wants to find

I haven't read the da vinci code, but you might want to see:

http://www.maa.org/devlin/devlin_06_04.html

and an article he mentions,

Markowsky, G. "Misconceptions About the Golden Ratio." College Math. J. 23, 2-19, 1992.

it's available in jstor, or fuzzy pdf version for those with no jstor access: http://www.dur.ac.uk/bob.johnson/fibonacci/miscons.pdf

Phi is real. Just type it in on google.

Phi is also a real number, and not imaginary or complex (har har har.) It is the positive number at which the ratio of lines "a" and "b" is the same as (a+b)/a. It works out to be a quadratic equation, which when factored has roots 6.180339887 and -1.618033989.

Phi is also a real letter in the Greek alphabet. It's name is pronounced "phee" in modern Greek, but it's called "ph-eye" in the scientific/mathematical context.

Phi exists in nature. But not to the extent that the Da Vinci Code suggests. There are some flowers and shells etc which have patterns related to phi through the fibonacci sequences (in which the difference between two consecutive terms approaches phi). But there are others which show patterns related to other sequences which follow similar rules.
eg. 1, 3, (1+3=)4, (3+4=)7, (4+7)=11 etc
0, 2, (0+2=)2, (2+2=)4, (2+4=)6
I don't know whether those particular series have any examples, but there are similar sequences which do.
And there are plenty of things which bear no relation to any of these series.

Yes, phi exists. In fact, as the Fibonacci sequence tends to infinitey the the ratio between any term of the sequence and its preceding term approach phi, i.e., where is just some term in the Fibonacci sequence.

I haven’t read or seen any of the ‘Davinci Code’ stable, and I’m an atheist, but I have to say that ‘phi’ is the most interesting thing I’ve ever come across in Nature/math.

Look into it. It’s a lot more than heresofar has been suggested. If there was something that would make me go ‘oohhh…’, this is it.

To add a little bit (having read the book and not been awfully impressed), particularly to Jacques' note on the limitations on the application of phi in nature, the greatest exaggeration by Dan Brown in the book regarding phi is what he says about its application to humans.

It is true that in his famous Vitruvian Man Da Vinci deliberately used the golden ratio but it is not, or cannot, be true that it necessarily applies to all humans. People are differently proportioned, and, as we all know, change in proportion even during the course of a single day - by up to about 1%. Therefore there is no way a ratio of even 1.618 could be considered accurate with regard to human proportions. At best you might claim an accuracy to about 1.6 to 1. But this number is definitely not phi - you might as well say that the ratio in length of the kilometre to the mile was mystically chosen to match ratios in the human body.

Sorry if this sounds a bit garbled, but I've been a fan of the Fibonacci ratio for some years now, and while it is a remarkable number, some of the claims made for it are greatly exaggerated.

As I recall also, a recent (admittedly internet based) study of classical artworks seems to show that viewers don't necessarily experience greater 'beauty' in art which closely matches the famed golden ratio compared with art that does not conform to it. So, despite Da Vinci and others probably using it in their art, it doesn't seem to make a discernible difference to the viewing experience.