AzBilliards.com The Mathematical Theorem Behind Poolology
 User Name Remember Me? Password
 Page 1 of 4 1 23 > Last »
 Share Thread Tools Rate Thread
 The Mathematical Theorem Behind Poolology
 (#1) BC21 Poolology     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

(#2)
goettlicher
AzB Silver Member

Status: Offline
Posts: 458
vCash: 500
iTrader: 0 / 0%
Join Date: May 2006

09-24-2020, 08:43 AM

Quote:
 Originally Posted by BC21 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

(#3)
BC21
Poolology

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 Great explanation! Randyg
Thanks Randy!

 (#4) bbb AzB Silver Member   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
 hats off
 (#5) Ratta Hearing the balls.....     Status: Offline Posts: 3,560 vCash: 2000 iTrader: 1 / 100% Join Date: Sep 2009 Location: germany 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"
(#6)
BC21
Poolology

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 Brian, extremly well presented knowledge Brian. Very well done mate! take care, Ingo
Thank you very much!

 (#7) Bob Jewett AZB Osmium Member     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. 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. Bob Jewett SF Billiard Academy Last edited by Bob Jewett; 09-25-2020 at 12:27 PM.
 (#8) BC21 Poolology     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.
(#9)
Dan White
AzB Silver Member

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 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

(#10)
BC21
Poolology

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 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.

(#11)
Dan White
AzB Silver Member

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 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

(#12)
Bob Jewett
AZB Osmium Member

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 .. 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

 (#13) straightline AzB Silver Member   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.
(#14)
BC21
Poolology

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 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.

(#15)
BC21
Poolology

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 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.

 Page 1 of 4 1 23 > Last »

 Thread Tools Rate This Thread Rate This Thread: 5 : Excellent 4 : Good 3 : Average 2 : Bad 1 : Terrible

 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 Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Main Category     Main Forum     Live Stream Area     Wanted/For Sale         For Sale Items         eBay Auctions         Wanted     Room Owner Discussion     14.1 Pool     Canadian Pool     Snooker     Carom Billiards     Memories of Steve Mizerak     English Pool     Billiard and Pool History in the U.S.     BEF Juniors Pool     Test Area     Cuesports: Rules & Strategies     AzB Hall of Fame     Pool Room Reviews Tournament Talk     U.S. Tournament Announcements     European Tournament Annoucements     Asian Tournament Announcements     Super Billiards Expo     Junior National 9-Ball Championships     World Championships     US Open Championships     Derby City Classic/Southern Classic     BCA Pool League World Championships     US Bar Table Championship     WPBA     Matchroom Events     Eurotour     Other Tours & Events Products Talk     Pool Tables and Accessories Reviews     Cue Reviews     Cue and shaft reviews     Cue Case Reviews     Cue Machinery and Supplies     Cue & Case Gallery     Ask The Cuemaker     Cue Accessory reviews     Other Item reviews     Talk To A Mechanic Instruction & Ask the pros     Aiming Conversation     George 'Ginky' San Souci     Instructional Material reviews     Instructor Reviews     Melissa Morris     Sarah Rousey     Ask The Instructor

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.

 -- Azb v4 -- Tech Two -- iPhone -- Test Style -- Default vBulletin -- AzBilliards vB 3 Style Contact Us - AzBilliards.com - Archive - Top