I think this may be grade school geometry now
Just to be clear...
So there is a “shot line”. This is the line from the resting spot of the cueball to the location it will be at impact. With a centerball hit, this will be a straight line.
Now are you claiming that people can, say for right English, move their whole cue over say a tip or 2 distance, keeping it parallel to the shot line? And pocket balls?
KMRUNOUT
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Absolutely, and you know it too. If we call the line we shoot the cue ball down with no english the target line, that is the most common frame of reference almost everyone uses. Can I move the tip over and keep it absolutely parallel in the horizontal plane and pocket the ball? Sure, adjust speed so that swerve and squirt cancel each other out for that particular shot, no slight angle corrections needed.
What we usually do if we use any form of side is also make a slight adjustment to correct our target path so that it intersects the target line at the object ball.
So, we can correct with speed, we can correct with tiny adjustments to the cue stick. This is required with all forms of side to arrive at a point on the target line and at the object ball at the same time. That point on the object ball needs a designation so lets call it point P. Point T will be where we hit the cue ball. Point T can be any contact point but for simplicity lets say it is at one tip of side for this discussion. The only important thing to understand is that we are talking about one point on the cue ball using all forms of side spin or english, whatever term is preferred.
Hopefully we can agree that only one line passes through multiple points on that line. A line is unique and defined by any two points on that line.
Now lets look at back hand english, front hand english, and parallel english. Back hand english pivots at our bridge and our grip hand moves sideways. There is a point on our target line that the cue stick pivots around at our bridge. Call this point A. After the pivot the cue lays on a line AT.
Now lets consider front hand english. The grip stays on the target line, the bridge hand moves. We will call the pivot point on the target line that front hand english moves around point B. This is at the grip hand. The line formed by the cue is line BT.
We have two lines angling across the target line at roughly twelve inches from the tip and fifty inches from the tip. We already have a problem with geometry here, it is impossible for AT and BT to be the same line. The basic theory that all three methods get the cue stick to exactly the same position is already proven false.
A parallel shift is a bit trickier to work with because we now move completely off the original target line. Our grip hand has moved, our bridge has moved, only point T which can have an infinite number of lines through it remains the same. However we will label a point somewhere on the parallel shift line point C and state as a given that point C is neither on the AT or BT line.
Now we have three lines by the much beloved math. AT is not equal to BT is not equal to CT.
A simple proof by math that the cue is not on the same line with front hand, back hand, and parallel english. This is easily discovered on the table if you put some notebook donuts down and use a striped ball to have the same target on the "cue ball", the edge of the line turned vertical. We quickly find that if we hit T on the AT line, the BT line, and the CT line, our math is confirmed. We get different results as has to happen according to the theory and math.
No easy way to draw and no way to get drawings into my computer. When I had CAD I could have drawn this in less time than it takes to type it. Easier for you to test on the table than to work through the logic since I had to go into painful detail using only text. It is really as simple as if you pivot off of the original target line in different places it has to create different lines. Also some basic geometry that a parallel shift will create a different line than a pivot.
Hu
Hu
