There's more to composition than the rule of thirds.
And Fibonacci's not an opera singer. (You're thinking of Pavarotti -- or of Bocelli -- or of no opera singers because why would you be?) The composition is the frame and the arrangement of the elements in that frame. What are the elements of a frame? The mise-en-scène -- everything in the frame that makes up the frame, including everything from the actors, to lighting, to props, to costumes, to composition.
Those two things, composition and mise-en-scène, are usually the first concepts you should (and do) learn about aesthetic theory, because they lay the foundation for everything else. But let's rewind for a second and take a look at what composition actually is and how the elements within the concept come into play when setting up and blocking your shots. Andrew Price breaks things down nicely in this video, which is geared toward CGI artists. However, don't be deterred if you're not one -- compositional principles are quite universal, applying to film, photography, painting, sculpture, and other plastic arts.
Understanding how to arrange the elements in your shot to create beautiful compositions is the foundation of your job as a filmmaker and cinematographer. Think of a film as a form of communication: the compositions (as well as editing, music, dialog, etc.) are our language and the elements of mise-en-scène are our words. Being able to comprehend them and know what they mean will only make you a better communicator, allowing you to express yourself fully through your film to your audience.