John_F Loc: Minneapolis, MN

Just crop to whatever suits your fancy and then run the calculation to see how close your crops come to the Golden Ratio. It will be hit or miss, to be sure.

Jagnut07 Loc: South Carolina

Boy, Now I am confused:

I read the formula above as C(C-A) = C^2

Transposing this is: (C-A) = C^2 / C

Which is (C-A) = C

So then C-C = A

Therefore A = 0

How can this be? Confusing. Maybe age is getting the better of me. Either that or I have nothing better to do :-)

Mike.

OhD Loc: West Richland, WA

The inverse of the golden ratio is about 1% smaller than 5/8, which is a nice rational number, hence the popular 5x8 crop ratio (a lot easier to measure than 1/1.618 which happens to equal 0.618).

The popular ratio 9/16 for wide-screen displays is the ratio of the two square sides of a Pythagorean right triangle 3:4:5 FWIW.

I'm not sure how standard paper sizes came to have the aspect ratios they have. Drafting/photo paper sizes starting at 8.5 x 11 are close to the golden ratio at ~.65 and each increasing size increment doubles the area, but why 5x7 and 4x6?

I tend to crop 9:16 because I like the look and I mostly view pictures on a screen anymore. I wish it was a standard metal print ratio.

Architect1776 Loc: In my mind

Correct.
We learned this is Architectural design.
It is a guide to know about but is NOT a rule to be religiously followed mindlessly.
Same in ALL composition understand as a concept but you are foolish to force the rule upon the design unless there is specific way the rule applies.
Bottom line you must use intelligence and experience rather than blindly follow a rule in the realm of design.

suntouched Loc: Sierra Vista AZ

:)

OhD Loc: West Richland, WA

The correct conditions are c=a+b; c/a = a/b; a>b. The derivation I read is:

Let the ratio a/b = f =c/a. (The Greek phi is customarily used, but not on my tablet keyboard, so "f" it.)

(a+b)/a = a/b
1+b/a. = f
1+(1/f) = f
0 = f-1-(1/f )
0 = f^2 - f -1. This is a quadratic with coefficients c1=1, c2=-1 and c3=-1, the roots of which are

f1 = (c2^2 + sqrt(c2^2-4(c1×c3))/(2×c1) and f2 = (c2^2 - sqrt(c2^2-4(c1×c3))/(2×c1)

Plug in the coefficients to get

(1+sqrt(5))/2 and (1-sqrt(5))/2. The second root is negative: -0.618, and therefore meaningless for a ratio of positive lengths. The first root is 1.618 =c/a and it's inverse is 0.618 = a/c.

iDoc Loc: Knoxville,Tennessee

Amen!

Architect1776 Loc: In my mind

Totally meaningless in real meaningful design.
No feeling or thought required, sounds like an engineer rather than a creator of design.

Curmudgeon Loc: SE Arizona

I have a headache now I'm going to bed.

OhD Loc: West Richland, WA

I'd differ with that most firmly. Consciously using specific proportions in composition requires knowledge and thought, and a great deal of both are evident in artwork that has been recognized as being exceptional and worth preserving for nearly as long as people have been engaging in artistic expression. Using "classical" proportions won't guarantee good art - that also requires that one have some vision, if you will, of an image that will mean something to and engage the viewer and the technical skill to realize that image. In our case, we can either compose a static image by manipulating viewpoint, subjects, lighting and, of course, how our camera will render all that in a file (DOF, color balance, ...), or we can see and capture a transient instant from our environment. In either case, we can refine many aspects of the image in post-processing, particularly, for the purposes of this discussion, the composition. Selective cropping to the most appropriate aspect ratio and placement of the subjects can transform an image from, to use an analogy, a muddled shaggy dog story to a punchy one-liner or a memorable aphorism. Using classical proportions in the composition, if and as appropriate to the image, will be apparent to viewers who have the knowledge to notice and appreciate it, and some elements of composition can be effective to enhance the feeling intended by the artist.

I don't think there's any formula that can be applied mindlessly to produce great art, but an artist may well use sophisticated calculation, color theory, symbolism drawn from a vast body of literature, philosophy, religion, science or sport, and even engineering to inspire, inform and enable the creative process. Some engineers can also be creators of design and vice-versa. Leonardo da Vinci, for example, was a pretty capable engineer for his time (engineering was barely a discipline then) and no slouch with any of the above-mentioned resources, and he has a pretty good reputation as an artist (for quality if not quantity or timeliness).

I don't think the OP was specifying that the golden ratio is the one cropping ratio one should use to make a good image, but just sharing something interesting.

Architect1776 Loc: In my mind

How many permanent designs across the nation have you created that are used by 10's of thousands of people, inside and out, who love the design and comment on it?

OhD Loc: West Richland, WA

None. Permanent is a rather ambitious claim. Da Vinci designs have been loved by hundreds of millions and commented on at book length by many over nearly 500 years. Looking at his work and the preparatory sketching, one can reasonably infer that the study of proportion, among many other subjects, might be useful to an aspiring artist in any medium.