Phi ratio on various projects

[sorveltaja]

Phi ratio - 1.61803. Also known as "golden ratio". Is there any possibility, that it could be used by someone like me, wannabe non-scientist type?

Leonardo Da Vinci has mastered the use of it on his paintings.

I recently read a two part ebook, that have so much information on them about the subject, that it goes far beyond my knowledge(mathematically).

When I read that kind of stuff, I'm very critical, also open-minded, as i'm usually not into those 'new age' things generally.

[mklotz]

The golden ratio is hardly "new age" stuff given that it's been around since the days of classical Greece.

It shows up in many places in nature and mathematics.  For example, the ratio of adjacent terms in the Fibonacci series approaches phi.

If you break a stick such that the ratio of the length of the small piece to the large piece is the same as the ratio of the large piece to the original stick, the ratio will be phi.  Which is just another way of saying that phi satisfies the curious relation:

phi - 1 = 1/phi

which means that phi is the solution to the equation:

x^2 - x - 1 = 0

or:

x = phi = [1 + sqrt(5)]/2

As to practical uses, whenever I have to lay out a rectangular base for an engine and there are no other constraints, I make the ratio of the sides phi.  The Greeks claimed this was the most pleasing shape to the eye.  I'm not sure the superlative is warranted but it does make a nice shape.  Other "rectangular" spacings are possible as well, e.g., the ratio of the spacing between support columns and their height.

[sorveltaja]

That 'new age' conclusion/term was purely made by me, and not to be confused with actual laws of mathematics/physics.

Fibonacci was also mentioned on those ebooks, that I read.

Also the flower of life...http://peggymarie010.files.wordpress.com/2010/03/flower-of-life.gif

Considering that book, even the ancient pyramids were built using that very phi ratio.

[Chazz]

I don't know if it's the same anilmal, but years ago when I made some custom speaker cabinets, the build book said to use "The Golden Ratio" for the cabinet dimensions, somthing like .6 to 1 to 1.6 (can't remember exactly).

Cheers,
Chazz

[sorveltaja]

Chazz, thanks for bringing a practical view. Phi/golden ratio affects also to audio world, based on what I've read.

What makes that Phi/golden ratio so specific?