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I am not a math specialist but I have to try to expalin some things about the number Phi. I hope I can help you a little on getting a general idea...
Searching for the best way to devide the length of a line, ancient Greeks tried to devide it in a way that the smaller part would be compared to the begger, as the bigger would be compared to the total length.
Let's see if we can see it some simpler on the next shape:
The part ΒΓ is as smaller from the ΑΒ as smaller the ΑΒ is, compared to ΑΓ.
ΑΒ / ΒΓ = ΑΓ / ΑΒ = Φ = 1.618...
This number, even if it is refered as ancient greek invention, it can be found very often to nature, if we observe flowers, shells, trees, even in the human body and of course in art.
If you need the mathematical way to calculate the number Phi, you can find it as Fibonacci number.
Let's see how it is calculated:
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1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 8 + 13 = 21 13 + 21 = 34 21 + 34 = 55 34 + 55 = 89 55 + 89 = 144 89 + 144 = 233 144 + 233 = 377 233 + 377 = 610 377 + 610 = 987 610 + 987 = 1597 987 + 1597 = 2584 1597 + 2584 = 4181 2584 + 4181 = 6765 4181 + 6765 = 10946 6765 + 10946 = 17711 10946 + 17711 = 28657 κλπ. |
3 / 2 = 1.5 5 / 3 = 1.66 8 / 5 = 1.6 13 / 8 = 1.62 21 / 13 = 1.615 34 / 21 = 1.619 55 / 34 = 1.617 89 / 55 = 1.618 144 / 89 = 1.6179 233 / 144 = 1.61805 377 / 233 = 1.618025 610 / 377 = 1.618037 987 / 610 = 1.618032 1597 / 987 = 1.6180344 2584 / 1597 = 1.6180338 4181 / 2584 = 1.6180340 6765 / 4181 = 1.61803396 10946 / 6765 = 1.61803399 17711 / 10946 = 1.618033985 28657 / 17711 = 1.6180339901 κλπ. |
As you see in every new sum, we sum the results of the previus two sums. Dividing each sum to the previous one is giving an increasing accuracy result of the number Phi.
A good aproach of number Phi is : 1.61803398874989484820458683436564...
Another method of calculating Phi is from the formula : (1+(sqr5))/2
I got bored with all these numbers...
Take a look at the fingers of your hand. Are you sure you know them good enough?
Each finger has three parts. The middle part is 1.618 times shorter than than the part before it and 1.618 times longer than the edge one. Now check your hand from the shoulder, the same way. Do the same with your legs. Measure whatever else you like and you can find many interesting gold ratios on your body!
But don't get so proud about it because it the same on many other creature in nature, as on plants too. If I wouldn't be so lazy to write some more about the shematic parts of number Phi, you could understand better what I am talking about, but if you search for 'golden mean' over the internet you can find people that can explain it much better than me!
For more infromation and related links, take a look at http://www.bigwig.net/nook/phi.htm
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