Go Back   AzBilliards.com > Instruction & Ask the pros > Aiming Conversation
Reload this Page The Mathematical Theorem Behind Poolology
Reply
Page 1 of 4 1 23 Last »
 
Share Thread Tools Rate Thread
The Mathematical Theorem Behind Poolology
Old
  (#1)
BC21
Poolology

BC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond repute
 
BC21's Avatar
 
Status: Offline
Posts: 4,164
vCash: 500
iTrader: 2 / 100%
Join Date: Feb 2017
Location: West Virginia
   
The Mathematical Theorem Behind Poolology - 09-24-2020, 06:49 AM

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
  
Reply With Quote

Old
  (#2)
goettlicher
AzB Silver Member
goettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond reputegoettlicher has a reputation beyond repute
 
goettlicher's Avatar
 
Status: Offline
Posts: 458
vCash: 500
iTrader: 0 / 0%
Join Date: May 2006
   
09-24-2020, 08:43 AM

Quote:
Originally Posted by BC21 View Post
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


P.B.I.A Master Instructor
2018 Instructor of the year
www.randygpool.com
  
Reply With Quote
Old
  (#3)
BC21
Poolology

BC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond repute
 
BC21's Avatar
 
Status: Offline
Posts: 4,164
vCash: 500
iTrader: 2 / 100%
Join Date: Feb 2017
Location: West Virginia
   
09-24-2020, 09:18 AM

Quote:
Originally Posted by goettlicher View Post
Great explanation!

Randyg
Thanks Randy!
  
Reply With Quote
Old
  (#4)
bbb
AzB Silver Member

bbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond reputebbb has a reputation beyond repute
 
Status: Offline
Posts: 7,668
vCash: 1700
iTrader: 46 / 100%
Blog Entries: 3
Join Date: Mar 2008
   
09-24-2020, 11:00 AM

just watched the first 5 minutes
have to go to an appointment
just brilliant brian
i will watch the rest tonight
  
Reply With Quote
hats off
Old
  (#5)
Ratta
Hearing the balls.....
Ratta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond reputeRatta has a reputation beyond repute
 
Ratta's Avatar
 
Status: Offline
Posts: 3,560
vCash: 2000
iTrader: 1 / 100%
Join Date: Sep 2009
Location: germany
 Send a message via ICQ to Ratta Send a message via MSN to Ratta  
hats off - 09-25-2020, 06:09 AM

Brian,

extremly well presented knowledge Brian.
Very well done mate!

take care,

Ingo


"You do not really understand something unless you can explain it to your grandmother."......Albert Einstein
________

"Advanced PBIA Instructor and proud member of the SPF Family"
  
Reply With Quote
Old
  (#6)
BC21
Poolology

BC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond repute
 
BC21's Avatar
 
Status: Offline
Posts: 4,164
vCash: 500
iTrader: 2 / 100%
Join Date: Feb 2017
Location: West Virginia
   
09-25-2020, 06:18 AM

Quote:
Originally Posted by Ratta View Post
Brian,

extremly well presented knowledge Brian.
Very well done mate!

take care,

Ingo
Thank you very much!
  
Reply With Quote
Old
  (#7)
Bob Jewett
AZB Osmium Member
Bob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond repute
 
Bob Jewett's Avatar
 
Status: Offline
Posts: 19,070
vCash: 1700
iTrader: 15 / 100%
Join Date: Apr 2004
Location: Berkeley, CA
   
09-25-2020, 12:12 PM

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.

Name:  CropperCapture[92].jpg
Views: 212
Size:  58.9 KB

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:
Name:  220px-ArcCapable.gif
Views: 251
Size:  22.1 KB

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.


Bob Jewett
SF Billiard Academy

Last edited by Bob Jewett; 09-25-2020 at 12:27 PM.
  
Reply With Quote
Old
  (#8)
BC21
Poolology

BC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond repute
 
BC21's Avatar
 
Status: Offline
Posts: 4,164
vCash: 500
iTrader: 2 / 100%
Join Date: Feb 2017
Location: West Virginia
   
09-25-2020, 12:50 PM

Nice geometry lesson Bob. It's 48.

Last edited by BC21; 09-25-2020 at 01:00 PM.
  
Reply With Quote
Old
  (#9)
Dan White
AzB Silver Member
Dan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond repute
 
Dan White's Avatar
 
Status: Offline
Posts: 4,603
vCash: 500
iTrader: 2 / 100%
Join Date: Oct 2005
   
09-25-2020, 01:14 PM

Quote:
Originally Posted by BC21 View Post
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.


Dan White
  
Reply With Quote
Old
  (#10)
BC21
Poolology

BC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond repute
 
BC21's Avatar
 
Status: Offline
Posts: 4,164
vCash: 500
iTrader: 2 / 100%
Join Date: Feb 2017
Location: West Virginia
   
09-25-2020, 01:39 PM

Quote:
Originally Posted by Dan White View Post
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.

Last edited by BC21; 09-25-2020 at 09:27 PM.
  
Reply With Quote
Old
  (#11)
Dan White
AzB Silver Member
Dan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond reputeDan White has a reputation beyond repute
 
Dan White's Avatar
 
Status: Offline
Posts: 4,603
vCash: 500
iTrader: 2 / 100%
Join Date: Oct 2005
   
09-25-2020, 02:08 PM

Quote:
Originally Posted by BC21 View Post

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.


Dan White
  
Reply With Quote
Old
  (#12)
Bob Jewett
AZB Osmium Member
Bob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond reputeBob Jewett has a reputation beyond repute
 
Bob Jewett's Avatar
 
Status: Offline
Posts: 19,070
vCash: 1700
iTrader: 15 / 100%
Join Date: Apr 2004
Location: Berkeley, CA
   
09-25-2020, 02:14 PM

Quote:
Originally Posted by BC21 View Post
.. 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.


Bob Jewett
SF Billiard Academy
  
Reply With Quote
Old
  (#13)
straightline
AzB Silver Member
straightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond reputestraightline has a reputation beyond repute
 
Status: Offline
Posts: 949
vCash: 500
iTrader: 0 / 0%
Join Date: Apr 2018
   
09-25-2020, 06:55 PM

I don't get how the math spawns a pool system. Divisive estimation? Pool presents exact interactions and results which are easily observed.
  
Reply With Quote
Old
  (#14)
BC21
Poolology

BC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond repute
 
BC21's Avatar
 
Status: Offline
Posts: 4,164
vCash: 500
iTrader: 2 / 100%
Join Date: Feb 2017
Location: West Virginia
   
09-25-2020, 08:46 PM

Quote:
Originally Posted by straightline View Post
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.
  
Reply With Quote
Old
  (#15)
BC21
Poolology

BC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond reputeBC21 has a reputation beyond repute
 
BC21's Avatar
 
Status: Offline
Posts: 4,164
vCash: 500
iTrader: 2 / 100%
Join Date: Feb 2017
Location: West Virginia
   
09-25-2020, 08:50 PM

Quote:
Originally Posted by Bob Jewett View Post
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.

Last edited by BC21; 09-26-2020 at 07:25 AM.
  
Reply With Quote
Reply
Page 1 of 4 1 23 Last »

Thread Tools
Rate This Thread
Rate This Thread:

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump



Powered by vBulletin® Version 3.8.9
Copyright ©2000 - 2020, vBulletin Solutions, Inc.
vBulletin Security provided by vBSecurity (Lite) - vBulletin Mods & Addons Copyright © 2020 DragonByte Technologies Ltd.