# The Mathematical Theorem Behind Poolology

#### BC21

##### Poolology
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Silver Member
I've read and heard some ignorant comments over the last 3 years concerning the "complicated" math with Poolology. Here's a video showing how the system was created, or at least showing the mathematical theorem that lead to the creation of the system.

A combination of math and physical experimentation was used to design and analyze system numbers, but when it comes to using the system there is no complicated math to perform, unless dividing double digit numbers in half is considered "complicated" for you.

Anyway, for those interested in how a simple mathematical approach was used to create a more advanced fractional aiming system, here it is....

Poolology and the Inscribed Angle Theorem

#### goettlicher

##### AzB Silver Member
Silver Member
I've read and heard some ignorant comments over the last 3 years concerning the "complicated" math with Poolology. Here's a video showing how the system was created, or at least showing the mathematical theorem that lead to the creation of the system.

A combination of math and physical experimentation was used to design and analyze system numbers, but when it comes to using the system there is no complicated math to perform, unless dividing double digit numbers in half is considered "complicated" for you.

Anyway, for those interested in how a simple mathematical approach was used to create a more advanced fractional aiming system, here it is....

Poolology and the Inscribed Angle Theorem

Great explanation!

Randyg

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Silver Member

#### bbb

##### AzB Gold Member
Gold Member
Silver Member
just watched the first 5 minutes
have to go to an appointment
just brilliant brian
i will watch the rest tonight

#### Ratta

##### Hearing the balls.....
Silver Member
hats off

Brian,

extremly well presented knowledge Brian.
Very well done mate!

take care,

Ingo

#### BC21

##### Poolology
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Silver Member
Brian,

extremly well presented knowledge Brian.
Very well done mate!

take care,

Ingo

Thank you very much!

#### Bob Jewett

##### AZB Osmium Member
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Silver Member
The inscribed angle theorem is one of the first really surprising theorems you run into in geometry class in high school or junior high school. I remember thinking, "What? Really?" when Mrs. Morgan showed it to us. Here is a diagram that illustrates the theorem and shows something else that is really remarkable and useful about the inscribed angles.

To restate the theorem: If you have any two points on a circle, such as X and Y which are at the ends of the red dashed line, the angle they form from any other point on the circle, such as P, R and even Q which is way out in left field, is the same. In this diagram, they are called angle A -- all equal.

The proof is not hard if you know just a little geometry, and there is a fairly clear proof on Wikipedia that only uses basic ideas. Here is an animated drawing shown there:

One way to think about this is that the distance between those points and the size of the circle determine all those angles completely -- no matter which third point you pick on the circle, you get the same angle. Of course if you make the circle larger with the same two points, the angle will get smaller and vice versa.

The second amazing thing I mentioned above is that if the third point you choose is the center of the circle, as in the drawing above marked C, then the angle the center sees out to the starting points X and Y (called the central angle), is exactly twice the angle A, which is the inscribed angle. This central angle is usually much easier to figure out than the inscribed angle.

Here's a simple question to see if you have followed all of this: What is the central angle between the balls two apart as in Brian's demonstration? Hint: all 15 balls of the rack are uniformly spaced around the circle.

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#### BC21

##### Poolology
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Silver Member
Nice geometry lesson Bob. It's 48°.

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#### Dan White

##### AzB Silver Member
Silver Member
I've read and heard some ignorant comments over the last 3 years concerning the "complicated" math with Poolology. Here's a video showing how the system was created, or at least showing the mathematical theorem that lead to the creation of the system.

A combination of math and physical experimentation was used to design and analyze system numbers, but when it comes to using the system there is no complicated math to perform, unless dividing double digit numbers in half is considered "complicated" for you.

Anyway, for those interested in how a simple mathematical approach was used to create a more advanced fractional aiming system, here it is....

Poolology and the Inscribed Angle Theorem

Great explanation! Now if a newbie used Poolology to aim and a laser to train a straight stroke I wonder how quickly we could create an A player!

Oh, and 48 degrees.

#### BC21

##### Poolology
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Silver Member
Great explanation! Now if a newbie used Poolology to aim and a laser to train a straight stroke I wonder how quickly we could create an A player!

Oh, and 48 degrees.

Thanks Dan, and great question! I'd say with a dedicated student it wouldn't take long at all, especially compared to old school trial and error methods.

And I suppose what Bob was pointing out with the geometry lesson is the fact that the template I made was not 30°. Lol. I posted a comment on the video after I uploaded it stating that the template was actually around 26°, not 30. I actually cut the little template out before remembering that I had that circular rack somewhere. The true inscribed angle between the 1 and 15 and any other ball, if calculated using that exact circle of balls, would be 24°. But it's irrelevant because the video is about why the system works, not about giving a precise geometry lesson for that particular circle.

Anyway, rather than going into all of the unnecessary details of why it's 26° instead of 30, I simply called it 30° in the video, because the shot angle used with that specific cb-ob relationship will be a 30° halfball shot every time.

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#### Dan White

##### AzB Silver Member
Silver Member
And I suppose what Bob was pointing out with the geometry lesson is the fact that the template I made was not 30°. Lol. I posted a comment on the video after I uploaded it stating that the template was actually around 26°, not 30.

I want my money back, pal!

I think we had it better than previous generations and future generations will have it better than we do. Pool instruction, that is.

#### Bob Jewett

##### AZB Osmium Member
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.. Anyway, rather than going into all of the unnecessary details of why it's 26° instead of 30, I simply called it 30° in the video, because the shot angle used with that specific cb-ob relationship will be 30° halfball shot.
I think it is better to have all the details in an explanation correct. Eventually you will run into a student who understands what you just said and why it was wrong. It is usually no more effort to have the details correct.

#### straightline

##### AzB Silver Member
Silver Member
I don't get how the math spawns a pool system. Divisive estimation? Pool presents exact interactions and results which are easily observed.

#### BC21

##### Poolology
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I don't get how the math spawns a pool system. Divisive estimation? Pool presents exact interactions and results which are easily observed.

Yes....exact interactions and results are easily observed. Unfortunately, they aren't quite as easy to perform.

#### BC21

##### Poolology
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I think it is better to have all the details in an explanation correct. Eventually you will run into a student who understands what you just said and why it was wrong. It is usually no more effort to have the details correct.

Good point, but any student who would understand or recognize that it's not an exact 30° angle for that particular circle of balls would also be smart enough to realize that such details are not important or relevant to the explanation. This video was simply showing how the system was created using a certain mathematical theorem. The exact angle of that template is irrelevant.

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#### straightline

##### AzB Silver Member
Silver Member
Yes....exact interactions and results are easily observed. Unfortunately, they aren't quite as easy to perform.

You simply shoot them. A competition rifle for instance is machined and calibrated to very fine tolerances as is the ammo. In pool the cue is already straight enough but it's up to the player to calibrate the act of shooting into spec. In most cases knowing where the stick goes and placing it there will eliminate most of the errors.

Did you mention you also play music? Same thing with a pool cue except simpler. One linear piston motion will cover the majority of it.

#### Dan White

##### AzB Silver Member
Silver Member
You simply shoot them. A competition rifle for instance is machined and calibrated to very fine tolerances as is the ammo. In pool the cue is already straight enough but it's up to the player to calibrate the act of shooting into spec. In most cases knowing where the stick goes and placing it there will eliminate most of the errors.

Did you mention you also play music? Same thing with a pool cue except simpler. One linear piston motion will cover the majority of it.

I don't think you understand the philosophy behind Poolology.

#### BC21

##### Poolology
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Silver Member
.......

....In most cases knowing where the stick goes and placing it there will eliminate most of the errors.

Did you mention you also play music? Same thing with a pool cue except simpler. One linear piston motion will cover the majority of it.

The statement in bold is simply not true. Most errors are stroke related, and for beginners or novice players finding exactly where the cue needs to be is also full of error because it's guesswork, estimation or trial and error.

If knowing exactly where the stick goes and placing it on that line were a simple task, all a player would have to do is develop a good and consistent stroke and the game would be easily mastered. But that's not how people learn to play pool. Instead, we find ourselves trying to develop two things at the same time -- aligning the cue consistently (aiming) and striking the cb consistently (stroke). If you were born with a perfect stroke, aiming skills would take no time. If you were born with perfect aiming skills, developing a consistent stroke would take no time. But we aren't born with either, so we have to develop both. What Poolology does is give the player a shortcut for the aiming portion of their development, which should make the stroke development come about more quickly.

And music is the same way. Sure, the piano or guitar is just waiting there ready to be played, but a person must first learn the skills needed to do it. As with pool, it's not simple. It takes a lot of work, a lot of skill development.

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#### straightline

##### AzB Silver Member
Silver Member
The statement in bold is simply not true. Most errors are stroke related, and for beginners or novice players finding exactly where the cue needs to be is also full of error because it's guesswork, estimation or trial and error.

If knowing exactly where the stick goes and placing it on that line were a simple task, all a player would have to do is develop a good and consistent stroke and the game would be easily mastered. But that's not how people learn to play pool. Instead, we find ourselves trying to develop two things at the same time -- aligning the cue consistently (aiming) and striking the cb consistently (stroke). If you were born with a perfect stroke, aiming skills would take no time. If you were born with perfect aiming skills, developing a consistent stroke would take no time. But we aren't born with either, so we have to develop both. What Poolology does is give the player a shortcut for the aiming portion of their development, which should make the stroke development come about more quickly.

And music is the same way. Sure, the piano or guitar is just waiting there ready to be played, but a person must first learn the skills needed to do it. As with pool, it's not simple. It takes a lot of work, a lot of skill development.

I already said the stroke must be linear. It's most adaptable that way. Getting there requires as much or as little calibration as is required. The stick is designed, configured, and manufactured to be as compatible with this task as practical. Why are you looking for fractions when the shot sits there motionless waiting on you to shoot?

#### straightline

##### AzB Silver Member
Silver Member
I don't think you understand the philosophy behind Poolology.

The suffix "ology" implies science. I think applying the sacred inscriptions to reveal pool is pretty cool; and, an extra step that leads away from exactitude into the world of uncertainties where perhaps these approaches can thrive.

Whatever, I'm here to question and learn not gratuitously bash.

I have an idea for your laser project. Duck tape a laser to the front end of a stick and stroke at a wall 5' away. I will bet it's not even close to a kill dot but whatever you get is what's wrong with your stroke. I've never tried this; could be 5" or 20'. Dun matter...

From there, add stroke jigs. Yeah, like the weight machines except stroke. Stick on rails etc...