The most basic mathematical principle of billiards aiming is the so-called "hemisphere method", as shown in figure 1, that is, the correct aiming point (point A) is on the extension line connecting the center of the ball bag and the center of the target ball, and it is one ball away from the center of the target ball (that is, the contact point with the surface of the target ball (point B) is half a ball away). No matter what the position of the cue ball and the target ball is, that is, how many degrees the angle α is in the figure, as long as you aim at the point A when hitting the ball, you can definitely send the target ball into the bag (of course, the angle α must be less than 90 degrees).

This method is also called "virtual ball method", because it can be assumed that there is a virtual billiard ball just tangent to the target ball, the connecting line between the two balls is aligned with the pocket, and the aiming point is the center of the virtual ball. Because the aiming point is on the extension line connecting the center of the pocket and the center of the target ball, it seems that this line has a tail half the length of the ball, so it is also commonly known as "finding the tail".

Example-Virtual Sphere Method:

1. Imagine an "imaginary ball" next to the target ball.

2. Don't aim at the contact point of the target when aiming.

3, but aim at the center of the "imaginary ball"