To prove our claims above, we are going to exploit this simple idea, the mirror being one side of the billiard table. A chaotic system will also move predictably towards its attractor in phase space - but instead of points or simple loops, we see "strange attractors" appear - complex and beautiful shapes (known as fractals) that twist and turn, intricately detailed at all possible scales. The behaviour of the system can be observed by placing a point at the location representing the starting configuration and watching how that point moves through the phase space. Phase space may seem fairly abstract, but one important application lies in understanding your heartbeat. Though we may not be able to predict exactly how a chaotic system will behave moment to moment, knowing the attractor allows us to narrow down the possibilities. The branch of fractal mathematics, pioneered by the French American mathematician Benoît Mandelbröt, allows us to come to grips with the preferred behaviour of this system, what is billiards even as the incredibly intricate shape of the attractor prevents us from predicting exactly how the system will evolve once it reaches it. It also allows us to accurately predict how the system will respond if it is jolted off its attractor.

The mathematician Ian Stewart used the following example to illustrate an attractor. She is a researcher in number theory and invents mathematical exhibits (for example the "Chinese Remainder Clock"). Scaling up the picture from the previous example by a factor of 3 then gives us this picture. If you’re familiar with Fermat’s principle of least time, then you can directly apply it here but with a billiard ball instead of light rays. Learn more about 8-ball here. So here we go, I didn’t know anything, but I was ready to do everything that I could to learn the sport. These 2 terms sometimes are used mistakenly because they all refer to cue sport using the cue sticks. Billiards is a cue sport played on a rectangular table with pockets, where players use cue sticks to strike balls into the pockets. In billiards, legal shots require the player to strike the cue ball with the tip of the cue stick, causing it to contact another ball.

However, the editors are always interested in amateur tournament reports from around the world, so feel free to send in results, descriptions and a contact source. Consequently, they are equipped with on-board computers which constantly and delicately adjust the flight surfaces to cancel out the unwanted butterfly effects, leaving the pilot free to exploit his own. Some players will purchase spot stickers and use them to mark out where the colored balls should go. The "on" balls are those that can be pocketed on any given turn. 1. If one of the two given numbers is a multiple of the other, what is the shape of the arithmetic billiard path? On a given turn, the rules determine which ball can be pocketed. What are the 8-ball pool rules? We know what makes a great pool table, and we know how much it should cost. Modern fighter jets achieve great manoeuvrability by virtue of being aerodynamically unstable - the slightest nudge is enough to drastically alter their flightpath. The purpose of a defibrillator - the device that applies a large voltage of electricity across the heart - is not to "restart" the heart cells as such, but rather to give the chaotic system enough of a kick to move it off the fibrillating attractor and back to the healthy heartbeat attractor.

No matter where it starts, the ball will immediately move in a very predictable way towards its attractor - the ocean surface. Once there it clings to its attractor as it is buffeted to and fro in a literal sea of chaos, and quickly moves back to the surface if temporarily thrown above or dumped below the waves. If released above the water it will fall, and if released underwater it will float. Certainly that will ensure fair play and help you to avoid unnecessary disputes during games. What happens if you play billiards on an elliptical table, with no friction? What happens if when you hit the billiard ball, it passes through one of the focus points of the elliptical table? Let’s take this further - what happens if we keep doing this? Are you having the same problems? Interestingly, what we get is an elliptical caustic curve that shares the same foci as the elliptical table, and so these are confocal ellipses. But we know from the aforementioned definition of the ellipse that any such path must have exactly the same length!