The below picture shows how we divide the image into 9 parts, and according to this rule we need to place the subject in the image at the intersections of these lines ( Red spots in the image below ).
The Rule of thirds is similar to the Golden Mean rule ( also know as the divine proportion). The theory is that if you place points of interest in the intersections or along the lines that your photo becomes more balanced and will enable a viewer of the image to interact with it more naturally. Studies have shown that when viewing images that people’s eyes usually go to one of the intersection points most naturally rather than the center of the shot – using the rule of thirds works with this natural way of viewing an image rather than working against it.The main reason for observing the rule of thirds is to discourage placement of the subject at the center, or prevent a horizon from appearing to divide the picture in half.
Look at the following links that explain about this rule
http://en.wikipedia.org/wiki/Rule_of_thirds
http://www.digital-photography-school.com/rule-of-thirds
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