A billiard aiming system includes a housing configured to be mounted to a ceiling above a billiards table; at least one sensor positioned within the housing and configured to detect a position and an identity of at least one object on a playing surface of the billiards table; and a projector positioned in visual communication with the billiards table and configured to project a grid on the playing surface of the billiards table. A system for teaching billiards includes a billiards table having a playing surface; the billiard aiming system, and a mobile device having a graphical user interface. The mobile device is configured to receive geometric data and identification data from the billiard aiming system and display instructions regarding a suggested shot trajectory on the graphical user interface based on the geometric data and the identification data.
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