Phi is my favourite number. It is roughly 1.61803399 and represented by the Greek letter…Phi. phi lower case is 0.61803399, or Phi -1. Like Pi it is an irrational number but it is also the solution to a quadratic equation.
Why am I blogging about it?
Because it’s a thought provoking subject, and it has inspired many people to try and use it in different ways. Maybe you will see a way of applying it to SEO or even SMM. Where is the golden ratio on Twitter? Can you see it in link distribution?
It’s an interesting number because it is also what we call “The golden ratio”, and also sometimes “The golden mean”, “section aurea” or the “golden section”. It was discovered over two thousand years ago phi by Euclid because of it’s crucial role in the shape of the pentagram. It can be found just about anywhere if you look for it, you’ll see it.
The Golden ratio is the total length A + B is to the longer segment A as A is to the shorter segment B. Or A is 1.618 … times B and B is 1.618 … times C
It’s: 1 / n = n – 1
or even: 5 ^ .5 * .5 + .5 = Phi
or if you’d rather: (sqrt(5)+1)/2
During the renaissance, artists, architects and so on were encouraged to use the golden ratio, because it made things more appealing to look at. Luca Paciolias wrote “De Divina Proportione” which inspired everyone to go ahead and make use of it. a result you’ll see in in Leonardo Da Vinci’s work, especially in the Vitruvian man
(named after Vitruvius) and even the Mona Lisa. Salvador Dali also used it, you can see it all over “The sacrament of the last supper“.
The Acropolis and the Pantheon are built to those proportions as are the pyramids and the Great Mosque of Kairouan. The architects Mario Botta, Leon Battista Alberti and Le Corbusier all used it in their buildings.
Musicians like Chopin, Debussy, Bartok and Satie all used it in their music.
You can find in geometry be it triangles, pentagons, dendograms… The DNA double helix forms a decagon, which is basically 2 pentagons, so it’s there too. Even the DNA molecule has Phi in it.
The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .The approximate ratio of each successive pair of numbers is Phi, for example 13/8 is 1.625 and 5/3 is 1.666 for example. When you get to the 40th number apparently it’s accurate to 15 decimal places.
It’s even been used to predict stock market fluctuations. Stephen Wolfram (who is receiving a ton of press attention right now due to his new search engine being released in May) studied this at length. In fact he wrote a book called “A New Kind of Science” which covers it and there’s information on his site as well. There’s also software designed to analyse the stock market based on Phi.
You’ll find it nature too, in sunflowers, broccoli, pineapples, pinecones, and flowers, leaves, fish, dolphins, even bugs.
It’s all over your body too!
If the length of the hand has the value of 1,then the combined length of hand + forearm is Phi. The proportion of upper arm to hand + forearm is also Phi (approx.). Your mouth and nose are both found at golden sections of the distance between the eyes and the bottom of the chin. Measure the distance from your shoulder to fingertip divided by elbow to fingertip. Try measuring your full height divided by the distance from your bellybutton to the ground.
Here is some computer code for you too in the form of the mathematica subroutine.
This video is easy to understand and also fun…all about Phi!
Phi really is a fun number that seems to turn up everywhere. To answer your question, though
> Where is the golden ratio on Twitter?
I’m not sure about Twitter, but it emerges pretty naturally on diffusion in Hanoi networks: http://arxiv.org/abs/0802.2757
Keep the interesting posts coming!
B
Thanks for the link to your paper Bruno, that’s really interesting. Do you think we can find instances where Phi is used on Twitter? Any ideas anyone?
“If the length of the hand has the value of 1,then the combined length of hand + forearm is Phi. ”
Given he’s explicitly defined Phi as 1.61803399, that would make a persons forearm shorter than their hand!
e^(i pi) = -1. This is amazing because e and pi are irrational and i is imaginary but they become an integer.
Hum, clearly got over excited writing this: the ratio of your forearm to your hand is approximately 1.618…
Great post! I have been afflicted with Phi for nearly 20 years now. Interestingly I have found practical application of the “sacred cut” in both SEO and web design.
I can’t remember the last time I saw something like that…bookmark ftw =)
Nice blog and thanks for the info!
Nice blog and thanks for the info!
Nice blog and thanks for the info!