THE GOLDEN RATIO
By dividing each number in the Fibonacci series by its predecessor, as we move to greater numbers it approaches 1.618033988749895, (1.61034, rounding) a number named Phi (Φ)
This number is unique in many ways. Looking again into the Fibonacci rectangle, its dimensions are proportionally these:
And it obeys Phi as follows:
A/B = B/C = 1.618034 = Phi, Φ, the Golden Ratio
For A=1, B = 0.618034, the Golden Mean and C = 0.381966
Now, 0.33 is approximately 0.38, so it looks like the Rule of Thirds is the simplified approximation of the Golden Ratio.
THE LEONARDO DA VINCI CONNECTION WITH FIBONACCI
It was not until around 300 years after Fibonacci wrote his Liber Abaci work, that Leonardo da Vinci came in contact with Phi. A mathematician friar named Luca Pacioli (1445-1514) asked Leonardo to provide drawings for his “Compendium de Divina Proportione” (Venice, 1509). Some scholars consider Leonardo as using the Divine Proportion in many of his works since then, solidifying a standard of beauty.
Phi IN ANTIQUITY
The further importance of Phi lies in the fact that long before Leonardo da Vinci it was studied and very possibly used to establish the proportions of buildings, sculptures and paintings of antiquity. For example,
Euclid of Alexandria – around 365 BC – 300 BC
Plato – around 428 – 350 BC
Phidias (500 BC – 432 BC), supervising architect of the Parthenon – 440 BC
Pythagoras the geometer 560-480 BC
From 3000 B.C., until nearly 300 BC
Pyramid of Giza – 2,560 BC
Harmonic principle - Khesi-Ra
Teotihuacan Pyramid of the Sun – around 300 BC
All of the above has been debated of course, partly because of some minor deviations in dimensions due to the effects of erosion. So whether you believe this proportion is divine or not, try it, you may like the results.
THE GOLDEN RATIO AND OUR NIKON CAMERA VIEWFINDERS
The bad news is that the viewfinders of our cameras do not have the right proportions and the focus brackets are not placed as needed.
Take for example these (L) image sizes:
D4: 4.928/3,280 = 1.502439
D800: 7,360/4,912 = 1.498371
D700: 4,256/2,832 = 1.502825
D7100: 6,000/4,000 = 1.500000
D610: 6,016/4,016 = 1.498008
All far from 1.618034
I don’t want to bore you with the standard sizes of printing paper; they of course don’t follow the Golden Ratio. We will therefore need to leave room to crop.
It can be done:
In closing, I would like to share an image sent to me by a very good friend, image that irrefutably proves the divine proportion is most pleasing to the eye and to the mind.
Have a great time!
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