Timeline for Does there exist a shot in ideal pocket billiards?
Current License: CC BY-SA 3.0
18 events
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| Sep 9, 2017 at 22:32 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image links broken; now fixed.
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| Nov 3, 2010 at 23:32 | comment | added | Joseph O'Rourke | @George: Your latest is simple enough to be verified experimentally, on a real pool table. Next time I have access, I will try. Even without that test, it is convincing. Clever! | |
| Nov 3, 2010 at 23:07 | history | edited | George Lowther | CC BY-SA 2.5 |
Typos
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| Nov 3, 2010 at 22:37 | history | edited | George Lowther | CC BY-SA 2.5 |
added clearer scenario
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| Nov 2, 2010 at 14:25 | vote | accept | Joseph O'Rourke | ||
| Nov 2, 2010 at 4:42 | comment | added | Daniel Litt | In any case, this clearly works if the balls are touching; I'm just quibbling over the case where they're not quite touching. But if the condition of scratching is indeed open, as I claimed in my answer, then this is clearly OK. So perhaps I should check that more carefully. | |
| Nov 2, 2010 at 1:25 | comment | added | Joseph O'Rourke | Although it is difficult for me to mentally run this scenario (a real billiard table would help!), if the 'T' of balls are all touching, the configuration (perhaps slightly varied) seems to work as you intend. Pretty slick, George! | |
| Nov 2, 2010 at 0:44 | comment | added | George Lowther | Well, I just changed the image to simplify it a bit but, in the new layout, you're suggest that cueing really hard slightly to the right and into the 4 is enough to divert the path. However, it should still move almost horizontally to the right (at least, for the ideal case). When the white hits the 4, it will move parallel to the tangent at the point of contact. | |
| Nov 2, 2010 at 0:39 | history | edited | George Lowther | CC BY-SA 2.5 |
modified the answer
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| Nov 1, 2010 at 23:51 | comment | added | Daniel Litt | I meant the following: hit the cue really hard, slightly upwards and into the 4. Then the cue hits the 4 but conceivably still goes to the right enough to hit the 3 without scratching, unless I'm being silly. | |
| Nov 1, 2010 at 21:04 | comment | added | George Lowther | Daniel. Imagine you have two circles of radius R which almost touch, but are a tiny distance x apart. What is the maximum range of angles of lines passing between them? A bit if trigonometry gives me $2\cos^{-1}(R/(R+x/2))\approx 2\sqrt{x/R}$. This is the maximum range of angles at which you can shoot the white directly towards the 3. | |
| Nov 1, 2010 at 20:45 | comment | added | Daniel Litt | Hmm...I am skeptical if the balls are not touching. It seems to me that if they are even just almost touching, one has enough control to go for the 3. That said, I agree this works if the balls are touching; this gives a rather interesting example in the vein of JDH's above. | |
| Nov 1, 2010 at 13:08 | comment | added | George Lowther | In that case, the cueball would stay put and the 2 and 4 move off at right angles to each other (assuming you avoid the push shot foul). I should add a couple more balls either side of the 15 so it doesn't move when hit by the 8. And credit Wikimedia commons for the table commons.wikimedia.org/wiki/…. I'll do that when I get a chance to log on later. | |
| Nov 1, 2010 at 10:28 | comment | added | Joseph O'Rourke | @George: Ingenious!!! And +1 for a beautiful illustration. I am worried if the cue ball is shot at $-45^\circ$ w.r.t. the horizontal. Would it really just behave the same for all downward angles? | |
| Nov 1, 2010 at 10:07 | comment | added | George Lowther | The point of having the balls almost touching is that the person cueing can't control the direction they go - only the speeds. The balls have to move in the pre-determined directions. | |
| Nov 1, 2010 at 10:04 | comment | added | George Lowther | I don't think so. Nothing should hit the 2, other than 10, which knocks it vertically downwards | |
| Nov 1, 2010 at 5:14 | comment | added | Daniel Litt | Hmm...you may want to require that the table is short relative to the (small) distance between the balls. Otherwise you can sink the 2, for example. That said, why can't one try to get the 3 in on a ricochet? | |
| Nov 1, 2010 at 4:05 | history | answered | George Lowther | CC BY-SA 2.5 |
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