Writing a blog has the advantage. In the past, it was just an idea that was too lazy to go deep. Through the step-by-step analysis of writing, you can slowly deepen your thoughts step by step, so that you can make some progress.

One idea was to scientifically quantify the aiming point of the billiard angle ball.

For billiards, if you want to play well, it is nothing more than playing it. What is the point to be hit, this requires a lot of practice to form muscle memory.

But for amateurs like us, we do not have so much time and energy to practice to form this memory.

Therefore, it is necessary to scientifically and systematically study the angle ball of the billiard ball.

Update: I wrote 2.0 version here.

Thinking of this, I took out the iPad Pro, ran Pro Create software, and started drafting a billiard table.

 



Just draw a white ball W, and a target ball T. Prepare to hit the T ball into the H hole. Now the question is coming, how do I calculate the angle of the ∠WTH.

The small white point of the pool table is the positioning star. We can know the angle of each positioning star by positioning the star.

 



The distances of the positioning stars are equal, that is to say, the long side of the billiard table has 8 segments ab long, and the short side has 4 segments ab long. Thus the angle of each positioning star is the geometric arctan of the junior high school.

∠glh = arctan(0.25)=14 degrees

∠flh = arctan(0.5)=27 degrees

∠elh = arctan (0.75) = 37 degrees

∠dlh = arctan(1)=45 degrees

∠clh = arctan (1.25) = 51 degrees

∠blh = arctan (1.5) = 56 degrees

∠alh = arctan (1.75) = 60 degrees

∠olh = arctan(2)=63 degrees

These 8 angles are enough to cover any angle change in billiards, so you need to remember.

 

Now let's go back to the first picture and show how to calculate the angle of ∠WTH.



We can know by drawing an extension cord:

The extension point T of HT almost coincides with 37 position, so the ∠O'HT angle is 36 degrees.

The extension point W' of HW is almost at the 51 position, so the ∠O'HW angle is 53 degrees.

Thus the ∠WHT angle is equal to 53-36 = 17 degrees.

We also need to draw a parallel line HH' of WT.

H' is almost a little more than two positioning stars. Compared with the long side, it is a little more than arctan (0.25).

From this, the angle of ∠OHH' is estimated to be a little more than 14. Calculated 16 degrees.

Then the angle of ∠H'HW=90-16-53=21 degrees

From this, the∠WTH angle = 180-21-17 = 142 degrees

However, when we aim at it, we don't need to calculate the obtuse angle. If we can directly calculate the acute angle, the ∠WTT' angle is 21+17=38 degrees.

The angle is calculated. The next question is coming:

How do we aim at the 38 degree angle?

Another picture

 



The T point is the pendulum point, the ∠THO angle is 45 degrees, and the Tab angle is arctan (2) is 63 degreee.

Then you can know that the angle of ∠aTH is 63+45=108 degrees.

We converted it to an acute angle of 72 degrees.

In the same way, we calculate that point b is a 45-degree angle.

Point c is 63-45 = 18 degrees.

The d point is 0 degrees. No need to consider

The e point is 45-arctan (2/3) = 45-33 = 12 degrees

The point f is 45-arctan (2/4) = 45-27 = 18 degrees. Just like c, just aim from the other direction.

The g point is 45-arctan (2/5) = 45-22 = 23 degrees.

h point is 45-arctan(2/6)=45-18=27 degrees

The i point is 45-arctan (1/6) = 45-9 = 36 degrees

So I put two balls on the pool table and took pictures.

 



This picture is from the point of view of point a, you should hit the white ball to enter the H hole. Keep in mind that this is a 72-degree angle cut.

Point b is a 45 degree angle. :



Point c is an angle of 18 degrees. The white ball covers about 2/3 of the black ball.



The e point is a 12 degree angle, covering the black ball more than 5/6



f points 18 degrees, skip. g point 23 degrees:



The h point is 27 degrees:



i point 36 degrees:



Well, these angles have already been introduced. In actual combat, you can train yourself to hit the black ball from these positioning stars to practice these angles.

I hope that everyone can still remember the eight angles which are 14, 27, 37, 45, 51, 56, 60, 63.

The basic geometry allows you to calculate the angle between the white ball and the target ball and the hole, so that you know where the aiming point is.

I believe that everyone can certainly improve the accuracy of playing through scientific calculations.