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Why the rule of thirds in photography?

J. Ramon Palacios (jrp)


Keywords: basics, composition, technique, theory

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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:

20140113_100428_picture7.jpg

 

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.

 

20140113_100428_picture8.jpg

 

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,

GREECE
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

EGYPT
From 3000 B.C., until nearly 300 BC
Pyramid of Giza – 2,560 BC
Harmonic principle - Khesi-Ra

MEXICO
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.

 

20140113_100428_picture9.jpg

Fellow Nikonian Chris Gray (wpgf100)

 

It can be done:

20140113_100428_picture10.jpg

 

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.

20140113_100441_picture11.jpg

 

Have a great time!
JRP

 

Got a Composition question?

You have a question regarding composition in your photography? No problem - just post your image or ask in our Post for critique forum.

 

Post a Composition Question

(16 Votes )
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Originally written on January 13, 2014

Last updated on January 24, 2021

J. Ramon Palacios J. Ramon Palacios (jrp)

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

San Pedro Garza García, Mexico
Admin, 46135 posts

22 comments

J. Ramon Palacios (jrp) on November 1, 2017

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

Frederick, I will place some samples for you in the A Picture I Took forum tomorrow morning, Nov 2.

Frederick W. Ming (optimist13) on October 29, 2017

Thank you for this article. I would be grateful if you (or another) could give a few more examples of compositional applications. Thanks Fred

Agli Olio (AgliOlio) on May 19, 2015

Happened to bump into this mind blowing article! Cool!

Andrew McDonald (AndyMac) on January 17, 2014

It's OK. I can take it and I learned a lot on that trip. :)

Bo Stahlbrandt (bgs) on January 17, 2014

One of the two c-founders, expert in several areas Awarded for his valuable Nikon product reviews at the Resources

This topic cannot be repeated often enough Ramón. Thanks for sharing this. Also love the thumbnail for this article on the homepage :)

J. Ramon Palacios (jrp) on January 16, 2014

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

I didn't want to bring that up, Andy ;-)

Andrew McDonald (AndyMac) on January 16, 2014

JRP, I was referring to the fact that I took them. I still remember the presentation you did. You pulled up the Rick picture as an example of good use of Rule of Thirds and I got all happy. Then you pulled up the image of Jon and I got all embarrassed.

David Clemmer (AMusingFool) on January 16, 2014

To get absurdly into Fibonacci's series: http://www.fq.math.ca/

J. Ramon Palacios (jrp) on January 16, 2014

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

Phillip, It is easier than one may think at first. Let's take this on at the forums.

User on January 15, 2014

Examples: [imglink:420488] and [imglink:420487] Both taken at 11mm to get entire church and the entire original part in the picture.

User on January 15, 2014

Not for Ghoulish reasons, but for Family Tree items (another interest on Mine). I Take Photos of churches associated with the deceased relatives, Grave stones Markers. If using the Rule of 3's how does one get the Whole of the Front or back of the Church in the field of view If not taken dead center on, although I have a 10-24mm Lens for my camera. At really wide angles such as 10-11mm just taking a Frontal Shot causes Perspective Issues example keystoning if the least bit below the church, and if straight on either the center or the edges appear to be closer.

Mathew Bunnell (trek) on January 15, 2014

It does not matter how much I think I know. I'm always humbled how much I don't. You guys amaze me!

Dane Dane (FFN) on January 15, 2014

Ribbon awarded for his generous support to the Fundraising Campaign 2014 Ribbon awarded for his generous support to the Fundraising Campaign 2017-2018

Yet another great article from JRP. Thank you for your contributions and sharing of your knowledge.

J. Ramon Palacios (jrp) on January 13, 2014

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

Yes, Andy. Those images were made at the the Smoky Mountains National Park in South Tennessee and North Carolina, ANPAT 6th ;-)

Andrew McDonald (AndyMac) on January 13, 2014

To clarify since I can't edit, I was talking about the images of Jon and Rick.

Andrew McDonald (AndyMac) on January 13, 2014

Gee, those photos look familiar. Both the good and the bad. :)

J. Ramon Palacios (jrp) on January 13, 2014

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

George, thank you. Yes, photography is quite challenging and remains to be no matter how much we may think we learn. That makes it always interesting and delightful, even when at times frustrating ;-)

J. Ramon Palacios (jrp) on January 13, 2014

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

Egbert, thank you. Indeed Euclid discovered the golden cut because of its crucial role in the construction of the pentagram. This has been accounted by now in several well document books by reputable authors. For example "The Golden Ratio: The Story of Phi, the World's Most Astonishing Number" also published in 2003, by Mario Livio, then senior astrophysicist and the Head of the Office of Public Outreach at the Space Telescope Science Institute (STScI) in Baltimore, MD.

J. Ramon Palacios (jrp) on January 13, 2014

JRP is one of the co-founders, has in-depth knowledge in various areas. Awarded for his contributions for the Resources

Jacques, merci. France indeed has many constructions that follow the Divine Proportion, for example Notre Dame de Paris cathedral. Furthermore, contemporary street photographers, like Henri Cartier Bresson ('father' of photojournalism) can be considered as making frequent and extensive use of the rule.

George Butterfield (Gbutterf1) on January 13, 2014

Thanks for a very interesting topic, composition has and continues to be one of my biggest challenges, that and light, speed, focus, lens choice, etc,etc.

Egbert M. Reinhold (Ineluki) on January 13, 2014

Thank you for the story. I have to add that Euclid found this rule. It was he who described the golden cut in the year 300 b.c. But the rule is even older but Euclid was the first seeing this in a pentagram.

Jacques Pochoy (archivue) on January 13, 2014

As for Architecture, the red and blue rules of "Le Corbusier" (or "Corbs"), follow exactly the 1.618 and 0,618 ratios respectfully... :-) Further testings, when asked to divide a segment non symmetrically, most people set up to a 1/3d ratio, which in french is called "tiercer" (divide by three), and most renaissance architecture as common farms buildings often have doors and windows proportions set by the one third ratio... :-) As all rules, they are meant to be overridden, If there is a good reason to it... As with DoF, it is often a mean to "disturb" the viewer and pinpoint a given situation of the subject !

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