75 SYSTEMS - 3 CUSHION BILLIARD by 75systems

Knowing Dbs, how we can calculate the Impact Thickness, Right of 1st Ob.

Dbs. System 1 Drawing

1st Ob

Numbering of the Aim Thickness on the Right Side of 1st Ob in Outside Hit 1st Ob

Cb 2,5 30

Outside Hit Right side

Impact Thickness = 2,5 (Is the contact point Between Cb & 1ης Ob)

-4

-3

-2

-1

After the impact, 1stOb will move in an Angle 300 relative to the direction Cb had before the impact, in the blue arrow’s direction. Cb after the impact will move in the red arrow direction. (Almost vertical to the direction in which 1st Ob will move).

Aim Thickness + English = Dbs (Dimitri’s ball system) Thickness Aim/2+English/4 = Impact Thickness No2

Impact Thickness = 2,5, we have in all of the following combinations of Dimitri’s ball system (Dbs) Abbreviation below: Abbreviation below:

Aim Thickness = Thick Impact Thickness = I.T

Thick + English 5 , +0 4 +2 3 +4 2 +6

= Dbs =>Thick/2 + English/4 = I.T = = = =

5 6 7 8

5/2 4/2 3/2 2/2

+0/4 +2/4 +4/4 +6/4

No4

No6

No0 English

= 2,5 = 2,5 =2,5 = 2,5

Aim Thickness = 5 English = 0 Dbs = 5 + 0 = 5 Textbook, page 51

System 1: Drawing 67: Dimitri’s ball system: Outside Hit Aiming Right side of 1st Ob: Example 1 Rail 0

Rail 3

Dimitri’s Diamond System

Dimitri’s ball system

Rail 2 Rail 1

Rail 3 Dimitri’s Diamond System

1,5 1

4,5 1

1st Ob 1 40

6,5

Aim Thickness Right side of 1stOb Outside Hit

8,5

Cb 1

9 35

1 6 4

English

2nd Ob

Dimitri’s ball system

45 4

2 1 1

3,5

4 6

7 Rail 0 8

Dimitri’s Diamond System

Terminal = 4,5 1st Ob’s Position = 3 - 1,5 = 1,5 Cb’s Position = 10,5 - Inclination = 10,5 - 6,5 = 4. Total sum {Dbs}

Rail 4 D s

Rail 4 {DDS}

Textbook, page 68 = 4,5 + 1,5 + 4 = 10 = Aim Thickness + English

{Dbs}: Section 3. System 4. {Big Snail} Cb  1st Ob  Short  Long  Short (See Drawings 86 to 89, Drawing Book, pages 73 to 76)

What we are looking for, when 1st Ob is a bit far from Cb, is what Aim Thickness to use in our aim with No-English, or what English we must use, in order to perform a {Big Snail} so that after Cb`s impact on 1st Ob, reach an exact point on Rail 3. Since the distance between Cb and 1st Ob is long, it is difficult to achieve the exact aim we want by hitting with English, because Cb makes a small curve until it impact on the 1st Ob (see General Observations). We could compare this system to the Dbs system (“small billiard”, which we have already developed), but with the differentiation of being played on the big billiard. We define accordingly the Numbering for the diamonds and the Correction factor (1st Ob’s position) on Rail 1, Rail 3 and Rail 4 (See Drawing 86, Drawing Book, page 73.) Notice: The Correction factor (1st Ob’s position) Numbering on Rail 4 starts at -1,5, because of the Mini Curve phenomenon.  Terminal: The point on Rail 3 that we want Cb to terminate, in order to make the 3cushion carom shot (that is, after its reflectance, to impact on the 2nd Ob).  1st Ob’s Position = 1st Ob’s Initial Position + Correction factor (1st Ob’s position) 1st Ob’s Initial Position: It is defined by the intersection of the tangent to 1st Ob, with the corresponding diamond of Rail 1. (Brown dashed line) (See Drawing 86, Drawing Book, page 73, Rail 1 diamond 1) That is, if we draw a line that is tangent to 1st Ob, and parallel to Rail 2, the set of diamonds between these two parallel lines is the 1st Ob’s Initial Position. (Caution: each diamond measures half a unit (0,5) similar to the numbering at Rail 1)  Correction factor (1st Ob’s position): We have divided the long cushion Rail 2 into areas with small brackets (area between the two gray parallel lines, starting from the small brackets). Depending on where 1st Ob is located, it receives a correction factor that results from the numbers above the brackets. The sum of the two numbers above defines the 1st Ob’s Position (See example in Drawing 86).

1st Ob’s Position = 1 - 0 = 1 97

System 4: Drawing 86: {Dbs} {Big Snail}: Example 1&2 Correction Factor

Rail 1

0,5

1,5

(1st Ob’s Position)

-1,5

+0,25

Obtuse angle = Negative (-) Inclination Acute angle = Positive (+) Inclination

Α 2nd Ob

1st Ob -0,25

-0,5

11 -0,75

Aim Thickness Left side of 1stOb

Inside Hit 3

-1

0 4

3 1 4

6 Rail 2

English

Dimitri’s ball system 4

2nd Ob 0

(+) Inclination 2 Diamond

4,6

10 5

6 6 6

7 7 8 6

9 1

Rail 0

Example 1&2: Cb  1st Ob  [1] Rail 3 2nd Ob

Rail 3

Textbook, page 97, 98

Terminal = 1, 1st Ob’s Position = 1- 0 = 1, Cb’s Position = 1,3 Χ Inclination = 1,3 Χ 2 = 2,6 Total sum {Dbs}= 1 + 1 + 2,6 = 4,6 = Aim Thickness + English

Choice: Aim Thickness = 4,6 & No-English(0)

Example 4: (See Drawing 196, Drawing Book, page 183) Cb has Departure [D=3,5], and we want Terminal = 7 on Rail 2. So, we know: Total Number of diamonds DT = 3,5 = Inclination (DA) + Inclination(AT) We have 3,5 diamonds in total, between Departure and Terminal (7-3,5 = 3,5). We are looking to find the Aim, {that is the Inclination (DA)}. From the table above, we derive that it is[2,5], because Departure is from D = 3,5 and we must take it into account. So we Aim from D = 3,5 with Inclination 2,5 diamonds. In this way the Aim results in A = 6 on Rail 1 .

That is, we add: => 3,5+2,5 = 6. So we Aim at [6] on Rail 1 with English Νο-6

Pay attention to the following way of thinking: In this example, in order to find where we need to Aim with English Νο-6, we will use the knowledge obtained from the {Bricole, rail first} with English Νο3, which has been analyzed elsewhere in this book. (See System 13, {DDS}: {Bricole, rail first} & {Small Snail}, Drawing 111, Drawing Book, on page 98) (It's a difficult problematic that combines two Systems.) That is, Cb strikes Rail 1 with English Νο-6, but because of its impact with the cushion it loses English (because it impacts with a reverse English). So, when reflected from Rail 1, its English have been reduced, because the cushion, during impact, added positive English No3 ,to the existing Cb negative English Νο-6. So, the result is: +3-6 = -3. => English Νο-3 But the negative English Νο-3, act as Positive English No3 in terms of impact on Rail 2. So we can imagine that it is, as if we are striking with Departure from [A = 22] with Positive English No3, and we know that we will have the Terminal [T = 17]. (See Drawing 196, Drawing Book, on page 183, (numbering in squares with a black dashed line). We know this from System 13 (see Textbook on page 130 and Drawing Book, Drawing 111, on page 98)

The combination of the knowledge of two different systems has provided a precise solution in the above difficult example.

232

System 65: Drawing 196: {Bricole, rail first}: With English Νο-6: Example 4 Cb(from Long)  Long Long  Short  1st&2ndOb

Rail 2

Rail 1 8

2,5 + 1 = 3,5

T=7

Inclination (DA) + Inclination (AT) =

Rail 0

1st Ob

7 T=17

2ndOb

A=6

2,5 +1 = 3,5

D=22 3,5 5 2,5

4 Cb

D=3,5 1

2 3 4

2 DT = Inclination (DA) + Inclination (AT)

English Dimitri’s ball system

= 2,5 + 1 = 3,5

1 9 8

-6

5 6

Rail 0 Inclination (DA) = 2,5 = Number of diamonds included between Departure and Aim Textbook, page 232 Inclination (AT) = 1 = Number of diamonds included between Aim and Terminal Inclination (DA) + Inclination (AT) = DT = 3,5 Total Number of diamonds between Departure and Terminal

2,5 + 1 = 3,5 183

Section 4: System 75. {Bricole, rail first}: Cb Aiming and impacting first on Rail 1 and then 1st Ob, how do we achieve the correct thickness desired in 1st Ob. (See Drawings 222 to 225, Drawing Book, pages 209 to 212)

Our scope: How can we determine with precision the exact point that Cb must Aim on Rail 1, by playing a Bricole, rail first? To better understand the logic of System 75, I have enlarged the size of the balls and the billiard table to twice the dimensions we have so far seen in other examples, as well as cropping the upper right corner of the billiard and showing it across an entire A4-sized page. In System 75 we will use the knowledge we acquired from System 0.9 (see, Textbook page 23, and Drawing 20 in Drawing Book, on page 13), on what English does the Cb acquire when impacting the cushion, and how does it behave when reflecting from the cushion in acute and obtuse angle. In all the examples we have visualized Cb’s movement with dashed lines (as if in slow motion, frame-by-frame) and in various colors, to aid the Player-Reader’s understanding.

Example 1: (See Drawing 222, Drawing Book, page 209). Cb(from short)  Long  1st Ob  Long  Short  2nd Ob We want to find the point on Rail 1 on which we have to Aim, so that after its reflection from the cushion, Cb will impact very finely on the inner side of 1st Ob (relative to Rail 1), and as a result, perform the carom shown in Drawing 222.

We have to follow the steps below: 1st Step: We conceivably position Cb right on the point we want it to impact with 1st Ob (Drawing 222, see the ball with the red dotted line), and we determine the point of contact between 1st Ob and the imagined Cb, and so, we find the point Α0. 2nd Step: Conceivably, we determine point A1, symmetrical to point A0 (relative to the center of Cb) which is identical to A2, that will come into contact with cushion Rail 1. 3rd Step: Conceivably, we determine point [Α], symmetrical to point A1 (relative to the cushion) (See bracket with black continuous line, and bracket with black dashed line). 254

System75: Drawing 222: {Bricole, rail first} how do we achieve the correct thickness desired in 1st Ob: Example 1

Rail 2

Rail 1

2nd Ob

10 Α1 Α

1st Ob Α0 Α2

1 0

2 3 4

Cb Α3

No-English(0) Dimitri’s ball system

9 8 7

5 6

Rail 0

Textbook, page 254

209