Many people are good at fighting, but they generally avoid chopping at large angles on the grounds that chopping is very difficult. This essence is also the simple mathematics above. What happens when you thin the ball. The radius ratio of the two concentric circles is 1 2, the center o represents the center of the target ball, and the outer circle naturally represents the place where the center c of the white ball may reach. Suppose we want the target ball to move in the direction of AO, that is, we want to push the center C of the white ball to point A. The difficulty here is that we need to control the hitting direction very accurately, because a small change in TCA angle will cause a huge change in TOA angle. In terms of quantity, if the angle TOA is θ and the angle TCA is φ, then when θ is small, φ is approximately proportional to the square of θ, just as when A is small, 1-cos a is approximately proportional to the square of sin a. One consequence of this quantitative relationship is that we allow the error of θ to be small in order to make the target ball enter the hole.