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I have been reading different articles on photo composition. These discuss rules of thirds, triangles, and golden ratio, each suggesting different and contradicting approaches. Some of them say to place the subject alongside lines, some inside triangles or rectangles, and some at the intersections.
So where exactly should I place the subject orpoint of interest in the following 3 rules?
Inside, intersections, or alongside?
The reason you see conflicting information when researching is because these rules are slippery. None of them have a strong backing in science, and their history in aesthetics is less important than in popular myth. There's no evidence whatsoever that anyone used the golden ratio in art before the 20th century, but people have heard the story so many times that they're often unwilling to believe it.
I've written some (detailed, researched, and referenced answers) related to these:
The basic theme is that someone has an idea for a formula for composition, a process which when followed will give scientifically better results without needing to use artistic judgment. Then, a bevy of historical works are analyzed and (through the magic of selection bias) brought out to prove that this technique was the secret of the ancient masters.
Since artistic judgment is a difficult skill, and baffling to many people (to some it comes naturally, but for others only after a great deal of time and effort, and for many people it seems to never "click"), the idea that there's a straightforward solution is very reassuring — like a lifeline dangled into the rough waters of making art.
Having grabbed on to that, it's hard to let go. Of course, many, many people are fine with the idea that the rules are only guidelines, but for others, the structure becomes almost religious, and whole complicated systems get built up around the original rule, both to expand it (like the idea that intersections of rule of thirds lines are "power points") and to relax the restrictions so that more examples comfortably fit (like the idea that a 3:2 aspect ratio is close enough to count as connected to the golden section).
So, to answer the question, the basic answer is: do what works best for the individual image you're constructing. Triangles, squares, and balanced divisions can be useful tools in a composition, but they're your tools, and you should use them in your way. If you find that you're really getting good results with a particular framework, cool! You can make that part of your own style. But you probably shouldn't package that up as a rule for other people — we've got enough of those already.
Those rules (and many more like them) are not actually rules, they are are more of an OK starting point.
That is, if you don't have any unique composition that works well with your current scene than placing the subject at about 1/3 of the way (or on the golden ratio line, a diagonal, triangle, etc.) in will create a more interesting image than if it's at the center.
Different scenes work with different compositions, basically, you have to choose the specific "rule" (or the specific version of the rule) that works for each specific image, sometimes (but not often) placing the subject at the center works better than all those rules.
Also, those rules are not accurate and are based on observation not science, placing something on a line or to the side of the line are basically the same and well within the "margin of error" of those rules.
They are less rules and more guidelines. If you are inexperience with composition then following the guidelines and looking at how others followed or broke the rules will aid you in becoming a better photographer. Depending on the shot it may be better to not follow the rules, but until one is more experienced both shooting and having critically evaluated other photos it is probably best to follow the rules to help you develop your eye for composition.
