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Learning the three-cut system with the Billiard Aim Trainer II
by Paul R. Turner, Billiard Aim Trainer II inventor   
Tuesday, 6 April 2010
The aiming system used by the world's most successful players in all cue sports is what the Billiard Training Company calls the "Three-Cut System." Simply put, it is the purest and most scientific aiming system there is, and it's based on pure geometry. There are really only three cuts you need to learn to master pocketing balls. They are: ¼, ½ and ¾ cuts. All other cuts shots are slight variations of these three.
The basis of this aiming system is to cut the object ball in four equal slices, beginning with a perfect slice down the middle representing two halves of a ball. (fig. 1)
Next, by again slicing the object ball in equal parts to the left and right of the ½ ball cut, creates the ¼ and ¾ ball cut.
Now that we have the object ball perfectly proportioned in four equal parts, how can this help us in pocketing balls? The answer becomes clear once we apply this knowledge to the cue ball by superimposing a cue ball over the object ball, as if both were flat paper balls.
But first let's establish one more important fact: on a perfectly spherical object like a billiard ball the only absolute reference point is it's edge. Absolute from the point of view of the observer, that is, which in our example, is from the point of view looking directly behind the cue ball at the desired object ball.
Now here is the magic. The far left and right edge of the object ball represents a perfect ½ ball cut. We can see this clearly by using our "paper" ball example (fig. 2). When we place our cue ball over the object ball, aligning the center of our cue ball with the edge of the yellow object ball, you will see that the edge of the cue ball is now perfectly aligned with the center line of the yellow object ball.
By shifting the paper cue ball to the left until its left edge aligns with the ¾ ball slice of the object ball, you will see that the center line of the cue ball is now 14 mm inside the right edge of the yellow object ball (fig. 3) and is aligned perfectly with ¼ ball slice. This is a ¾ ball cut shot.
By moving the cue ball in the opposite direction will now reveal to us that the center line of the cue ball is now 14 mm outside the right edge of the object ball (fig. 4) and that the left edge of our cue ball is aligned with the ¼ slice. This is a ¼ ball cut shot. The standard professional pool cue ball used is 2¼ inch or 57 mm wide, so the distance between these cuts would be 14 mm - the approximate width of your cue tip.
From the following diagram (fig. 5) we can see that a typical pool cue tip is 13 mm wide, and therefore a good reference when estimating the ¼ and ¾ ball cuts. Because the standard cue ball is 57 mm across, the distance between the these standard cuts is always about 14 mm. It may be hard to visualize a distance of 14 mm, but it is easy for any pool player to do this using the width of their cue tip!

The following diagrams show the degree angles that corresponds to the ¼, ½ and ¾ ball cuts:

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