I think I'm gonna get one of these and make some proposition bets:
https://www.youtube.com/watch?v=4KHCuXN2F3I
https://www.youtube.com/watch?v=4KHCuXN2F3I
Can you guess what happens if you shoot directly away from the hole in any direction?
pj
chgo
Yes, since the spot and the hole are symmetrically located (on the ellipse's foci), shooting from the spot banks into the hole and shooting from the hole banks across the spot and then banks into the hole.Assuming no English, my guess is it banks into the hole.
Gideon
Yes, since the spot and the hole are symmetrically located (on the ellipse's foci), shooting from the spot banks into the hole and shooting from the hole banks across the spot and then banks into the hole.
I think the main point is to demonstrate something about ellipses. Of course cushions don't work like mirrors, so the demonstrator has to explain why the original idea doesn't actually work very well.... Someone went to a lot of work to build a table to prove some point that could have easily been proven by using someone like John Brumback, or any of the Bank Shot Artists and a real table. ...
interesting, I guess that if you start with a ball that is NOT on the "foci" (and use no English), you positively cannot bank it into the hole
?
You need not start on a focus. Any shot along any line that extends through a focus will go in the hole.
So if you don't aim through one of the focus points initially, and you could hit an infinitely long shot, and assuming ideal rebound, would you eventually cross one of them? would the final path be the cb rolling around the perimeter? At some point in my early 40s my brain gave up on trying to see such questions through to the answer. Clickbait has made my brain go soft. I was better prepared for the zombie apocalypse a decade ago.
(I'm thinking rolling around the perimeter.... reduce to a circle and think about Spirograph. Which my daughter just got for her birthday. Which is probably in a pile with Xmas toys. Argh brain now tired)
There is a subfield of mathematics called billiards that is exactly about particles reflecting perfectly off boundaries and studying their paths. Those who collect real billiard books have to be cautious or they will end up with such books.... Without knowing anything at all about the math involved, we can figure out that all banks that cross a focus go into the hole, and any bank which doesn't cross a focus will NEVER go into the hole. Ignoring english, speed, etc... ...
There is a subfield of mathematics called billiards that is exactly about particles reflecting perfectly off boundaries and studying their paths. Those who collect real billiard books have to be cautious or they will end up with such books.
For example....
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I might have an extra copy of the above in case you lose your mind out of the extra hole.I need another physics book like I need another hole in my head, but I might be tempted...